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Dissertations / Theses on the topic 'Classical theory of fields'
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1
Roulstone, Ian. "Twister theory and the infrared problems of classical fields." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259829.
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Schritt, Dimitri. "Symmetries in quantum and classical field theories." Thesis, University of Canterbury. Physics and Astronomy, 2013. http://hdl.handle.net/10092/8032.
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The initial chapter of the thesis provides a review of Weinberg’s formalism for the derivation of quantum fields. The formalism is extended to allow for the derivation of quantum fields with more than one spin degree of freedom. It is conjectured that it may be possible to construct massive bosonic quantum field theories of any desired spin j that are consistent and unitary at all energies without the need for regulator terms by including j + 1
spin degrees of freedom: j, j - 1, down to j - j. The concept is then demonstrated in two subsequent chapters by the derivation of a quantum field with spin one and spin zero degrees of freedom followed the derivation of a quantum field with spin two, spin one, and spin zero degrees of freedom. Both field theories are found to be consistent and unitary at all energies without the need for regulator terms. The final two chapters are on unrelated topics. The penultimate chapter provides an explicit derivation of quantum fields for massless particles of spin one-half. In the final chapter, a derivation of the free-space Proca and Maxwell equations is provided via a consistent identification of the linear combinations of the classical fields of the (1,0) and (0,1) representations of the orthochronous
Lorentz group.
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Dolby, C. E. "A state-space based approach to Quantum Field Theory in classical background fields." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598590.
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This dissertation is concerned with a new formulation of fermionic quantum field theory in classical (electromagnetic or gravitational) backgrounds, which uses methods analogous to those used in conventional multiparticle quantum mechanics. Emphasis is placed on the states of the system, described in terms of Slater determinants, rather than on the field operator, ψ(x). The vacuum state 'at time τ', defined as the Slater determinant of a basis for the span of the negative spectrum of the 'first quantized' Hamiltonian H1 (τ), provides a concrete realisation of the Dirac Sea. By using the concept of 'radar time', I propose a generalisation of the concept of 'hypersurface of simultaneity', which can be applied to an arbitrarily moving observer in curved spacetime. This is used to provide a consistent particle interpretation for this observer, which depends only on the choice of observer and the background present, not on the choice of coordinates, the choice of gauge (in electromagnetic backgrounds) or the detailed construction of the observer's particle detector. It is also the first definition that does not rely on the spacetime possessing any convenient symmetries. I show that in the cases of a uniformly accelerating observer in flat space (Unruh effect), and a comoving observer in an exponentially inflating universe, my definition reduces to previously accepted definitions. Although this definition is necessarily non-local (no local definition of particle could possibly be consistent with the Unruh effect) I demonstrate with a simple example that this non-locality is only significant on scales of the order of the Compton wavelength λc = h/mc of the particle concerned. The general S-matrix element of the theory is derived in terms of time-dependent Bogoliubov coefficients, demonstrating that this follows directly from the definition of inner product between Slater determinants. The process of 'Hermitian extension', inherited directly from conventional multiparticle quantum mechanics, allows second quantized operators to be defined without appealing to a complete set of orthonormal modes, and provides an extremely straightforward derivation of the general expectation value of the theory. Applications of the formalism to pair creation in spatially uniform electric fields, and to the treatment of discrete symmetries, are presented.
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HERAT, ATHULA RAVINDRA. "CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060257141.
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Nguyen, Duc Tho. "Classical and semi-classical analysis of magnetic fields in two dimensions." Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S045/document.
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Ce manuscrit est consacré à l'étude de la mécanique classique et la mécanique quantique en présence d'un champ magnétique. En mécanique classique, nous utilisons un Hamiltonien pour décrire la dynamique d'une particule chargée dans un domaine soumis à un champ magnétique. Nous nous intéressons ici à deux problèmes classiques de physique : le problème de confinement et le problème de scattering. Dans le cas quantique, nous étudions le problème spectral du laplacien magnétique au niveau semi-classique dans des domaines de dimension deux: sur une variété Riemanienne compacte à bord et dans ℝ ². En supposant que le champ magnétique ait un unique minimum strictement positif et non-dégénéré, nous pouvons décrire les fonctions propres par les méthodes WKB. Grâce au théorème spectral, nous pouvons estimer efficacement les vraies fonctions propres et les fonctions propres approchées localement proche du minimum du champ magnétique. Dans ℝ ², sous l'hypothèse additionnelle d'une symétrie radiale du champ magnétique, nous pouvons montrer que les fonctions propres du laplacien magnétique décroissent de manière exponentielle à l'infini avec une vitesse contrôlée par la fonction phase de la procédure WKB. De plus, les fonctions propres sont très bien approchées dans un espace à poids exponentielThis manuscript is devoted to classical mechanics and quantum mechanics, especially in the presence of magnetic field. In classical mechanics, we use Hamiltonian dynamics to describe the motion of a charged particle in a domain affected by the magnetic field. We are interested in two classical physical problems: the confinement and the scattering problem. In the quantum case, we study the spectral problem of the magnetic Laplacian at the semi-classical level, in two-dimensional domains: on a compact Riemmanian manifold with boundary and on ℝ ². Under the assumption that the magnetic field has a unique positive and non-degenerate minimum, we can describe the eigenfunctions by WKB methods. Thanks to the spectral theorem, we estimated efficiently the true eigenfunctions and the approximate eigenfunctions locally near the minimum point of the magnetic field. On ℝ ², with the additional assumption that the magnetic field is radially symmetric, we can show that the eigenfunctions of the magnetic Laplacian decay exponentially at infinity and at a rate controlled by the phase function created in WKB procedure. Furthermore, the eigenfunctions are very well approximated in an exponentially weighted space
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Biswas, Ranajit K. "The classical theory of field evaporation." Thesis, Aston University, 1987. http://publications.aston.ac.uk/8080/.
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The field evaporation literature has been carefully analysed and is shown to contain various confusions. After redefining consistent terminology, this thesis investigates the mechanisms of field evaporation, in particular, the relevance of the theoretical mechanisms by analysing the available experimental data. A new formalism `extended image-hump formalism' is developed and is used to devise several tests of whether the image-hump mechanism is operating. The general conclusion is that in most cases the Mueller mechanism is not operating and escape takes place via Gomer-type mechanisms.
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Wüster, Sebastian. "Classical and quantum field theory of Bose-Einstein condensates /." View thesis entry in Australian Digital Theses Program, 2007. http://thesis.anu.edu.au/public/adt-ANU20070802.161045/index.html.
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Thesis (Ph.D) -- Australian National University, 2007.DVD contains movies in .mov (macintosh quicktime) and .mpg formats, providing additional visualisation of the material discussed in the thesis. It also contains the source files for figures within the thesis as well as sample numerical code that was used for the research. The accompanying .txt files provide a brief description of the movie and a link to the relevant part of the thesis. Also contains some files in pdf format.
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Wong, Chik Him. "A theoretical study on the static and dynamic transport properties of classical wave in 1D random media /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202007%20WONG.
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Matsuda, Hidefumi. "Shear viscosity of classical fields using the Green-Nakano-Kubo formula on a lattice." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263463.
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Wuester, Sebastian, and sebastian wuester@gmx net. "Classical and Quantum Field Theory of Bose-Einstein Condensates." The Australian National University. Faculty of Science, 2007. http://thesis.anu.edu.au./public/adt-ANU20070802.161045.
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We study the application of Bose-Einstein condensates (BECs) to simulations of phenomena across a number of disciplines in physics, using theoretical and computational methods.
¶
Collapsing condensates as created by E. Donley et al. [Nature 415, 39 (2002)]
exhibit potentially useful parallels to an inflationary universe. To enable the exploitation of this analogy, we check if current quantum field theories describe collapsing condensates quantitatively, by targeting the discrepancy between experimental and theoretical values for the time to collapse. To this end, we couple the lowest order quantum field correlation functions to the condensate wavefunction, and solve the resulting Hartree-Fock-Bogoliubov equations numerically. Complementarily, we perform stochastic truncated Wigner simulations of the collapse. Both methods also allow us to study finite temperature effects.
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We find with neither method that quantum corrections lead to a faster collapse than is predicted by Gross-Pitaevskii theory. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by Gaussian quantum fluctuations or finite temperature effects.
Further studies are thus required before the full analogue cosmology potential of collapsing condensates can be utilised.
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As the next project, we find experimental parameter regimes in which stable three-dimensional Skyrmions can exist in a condensate. We show that their stability in a harmonic trap depends critically on scattering lengths, atom numbers, trap rotation and trap anisotropy. In particular, for the Rb87 |F=1,m_f=-1>, |F=2,m_f=1> hyperfine states, stability is sensitive to the scattering lengths at the 2% level. We find stable Skyrmions with slightly more than 2*10^6 atoms, which can be stabilised against drifting out of the trap by laser pinning.
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As a stepping stone towards Skyrmions, we propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a ``hollow'' laser beam containing an optical vortex, which realises an optical tunnel for the condensate. Using realistic experimental parameters, we demonstrate numerically that our method can stabilise up to 9 vortex rings.
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Finally, we focus on analogue gravity, further exploiting the analogy between flowing condensates and general relativistic curved space time. We compare several realistic setups, investigating their suitability for the observation of analogue Hawking radiation. We link our proposal of stable ring flows to analogue gravity, by studying supersonic flows in the optical tunnel. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons, and discuss whether these could be employed to study extreme cases in analogue gravity.
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Beyond these, our survey indicates that for conventional analogue Hawking radiation,
simple outflow from a condensate reservoir, in effectively one dimension, has the best properties. We show with three dimensional simulations that stable sonic horizons exist under realistic conditions. However, we highlight that three-body losses impose limitations on the achievable analogue Hawking temperatures. These limitations vary between the atomic species and favour light atoms.
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Our results indicate that Bose-Einstein condensates will soon be useful for interdisciplinary studies by analogy, but also show that the experiments will be challenging.
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Noltingk, Duncan Spencer. "A histories approach to classical and quantum field theory." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396281.
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Cheong, Lee Yen. "Classical and quantum field theory in de sitter expanding universe." Thesis, University of York, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.516651.
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Stillwagon, Shannon Rae. "Potential field theory and its applications to classical mechanical problems." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=3290.
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Thesis (M.S.)--West Virginia University, 2003.Title from document title page. Document formatted into pages; contains xi, 149 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 135-149).
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McCloud, Paul James. "Symmetry in classical and quantum field theory : an application of the theory of jets." Thesis, King's College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321679.
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Ferreira, Jorge Nélio Marques. "On invariant Rings of Sylow subgroups of finite classical groups." Doctoral thesis, University of Kent, 2011. http://hdl.handle.net/10400.13/177.
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In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical
groups. We have successfully constructed presentations for the invariant rings for
the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic
group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained
a minimal generating set which is also a SAGBI basis. Moreover, we computed
the relations among the generators and showed that the invariant ring for these groups
are a complete intersection. This shows that, even though the invariant rings of the
Sylow p-subgroups of the general linear group are polynomial, the same is not true for
Sylow p-subgroups of general classical groups.
We also constructed the generators for the invariant elds for the Sylow p-subgroups
of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n
and q. This is an important step in order to obtain the generators and relations for
the invariant rings of all these groups.
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Bégin, François. "Hellmann-Feynman theorem in some classical field theories by François Bégin." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66205.
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Roa, Aguirre Alexis [UNESP]. "Type-II defects in integrable classical field theories." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102532.
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roaaguirre_a_dr_ift.pdf: 584228 bytes, checksum: a9374484aaeff9b04bf55be78fb96d03 (MD5)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Nesta tese discutimos as propriedades de integrabilidade das teorias de campo clássicas em duas dimensões na presença de descontinuidades ou defeitos tipo-II, principalmente usando a linguagem do formalismo do espalhamento inverso. Um método geral para calcular a função geradora de um conjunto infinito de grandezas conservadas modificadas para qualquer equação de campo integrável é apresentado, uma vez que seus respetivos problemas lineares associados são dados e suas correspondentes matrices do defeito são calculadas. O método é aplicado no cálculo das contribuições dos defeitos para a energia e o momento para vários modelos e mostramos a relação entre as condições de defeito integráveis e suas respevtivas transformações de Bäcklund para cada modelo
In this thesis we discuss the integrability properties of two-dimensional classical field theories in the presence of discontinuities or type-II defects, mainly using the language of the inverses cattering approach. We present a general method to compute the generating function of an infinite set of modified conserved quantities for any integrable field equation givent heir associated linear problems and computing their corresponding defect matrices. We apply this method to derive in particular defect contributions to the energy and momentum for several models and show the relationship between the integrable defect conditions and the Bäcklund transformations for each model
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Roa, Aguirre Alexis. "Type-II defects in integrable classical field theories /." São Paulo, 2012. http://hdl.handle.net/11449/102532.
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Orientador: Abraham Hirsz ZimermanBanca: Clisthenis Ponce Constantinidis
Banca: Harold Socrates Blas Achic
Banca: Andrei Mikhailov
Banca: Marcio José Martins
Resumo: Nesta tese discutimos as propriedades de integrabilidade das teorias de campo clássicas em duas dimensões na presença de descontinuidades ou defeitos tipo-II, principalmente usando a linguagem do formalismo do espalhamento inverso. Um método geral para calcular a função geradora de um conjunto infinito de grandezas conservadas modificadas para qualquer equação de campo integrável é apresentado, uma vez que seus respetivos problemas lineares associados são dados e suas correspondentes matrices do defeito são calculadas. O método é aplicado no cálculo das contribuições dos defeitos para a energia e o momento para vários modelos e mostramos a relação entre as condições de defeito integráveis e suas respevtivas transformações de Bäcklund para cada modelo
Abstract: In this thesis we discuss the integrability properties of two-dimensional classical field theories in the presence of discontinuities or type-II defects, mainly using the language of the inverses cattering approach. We present a general method to compute the generating function of an infinite set of modified conserved quantities for any integrable field equation givent heir associated linear problems and computing their corresponding defect matrices. We apply this method to derive in particular defect contributions to the energy and momentum for several models and show the relationship between the integrable defect conditions and the Bäcklund transformations for each model
Doutor
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Eakins, Jonathan Simon. "Classical and quantum causality in quantum field theory, or, "the quantum universe"." Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/10069/.
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Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed, and this in turn rephrases and removes the traditional Measurement Problem inherent in the Copenhagen interpretation of quantum mechanics. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure. The possible origins of observable physics, including physical objects positioned at definite locations in an arena of apparently continuous space and time, are consequently investigated for a Universe that incorporates quantum theory as a fundamental feature. Overall, a framework for quantum cosmology is introduced and explored which attempts to account for the existence of time, space, matter and, eventually, everything else in the Universe, from a physically consistent perspective.
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Rodriguez, Leo L. "Black-hole/near-horizon-CFT duality and 4 dimensional classical spacetimes." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1172.
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In this thesis we accomplish two goals: We construct a two dimensional conformal field theory (CFT), in the form of a Liouville theory, in the near horizon limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two dimensions black holes admit a $Diff(S^1)$ or Witt subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. These charges and lowest Virasoro eigen-modes reproduce the correct Bekenstein-Hawking entropy of the four and three dimensions black holes via the Cardy formula (Bl"ote et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two dimensions CFT's energy momentum tensor is anomalous, i.e. its trace is nonzero. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the four and three dimensions black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamics and statistical quantities for the non local effective action approach.
We also show that the near horizon regime of a Kerr-Newman-$AdS$ ($KNAdS$) black hole, given by its two dimensional analogue a la Robinson and Wilczek, is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The $s$-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence in the appropriate limits. We also compute the Hawking temperature of the $KNAdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.
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Gründing, Lukas [Verfasser], and Georgi [Akademischer Betreuer] Dvali. "Towards a microscopic description of classical solutions in field theory / Lukas Gründing ; Betreuer: Georgi Dvali." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1126968390/34.
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De, Lorenzo Tommaso. "Black holes as a gateway to the quantum : classical and semi-classical explorations." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0264/document.
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Depuis 1916, l'étude des Trous Noirs a soulevé des questions intrigantes. Seulement certaines ont été résolues. En effet, nous faisons face à des régimes où s’entremêlent la théorie quantique et l'espace-temps. Les TN comme porte d'entrée pour comprendre la nature quantique de la gravité. Ma thèse a été entièrement dédiée à ce domaine central de la physique théorique, avec pour but la compréhension la plus large possible des débats autour de ces questions. C'est ainsi qu'ont été produits des résultats originaux qui constituent le cœur de ce manuscrit. 1-Les surfaces de volume maximal des TN sont étudiées. Un TN astrophysique terminera sa vie avec une aire planckienne de $10^{-70} m^2$ dissimulant $10^5$ fois le volume de l'univers observable. Ceci peut avoir des conséquences sur la viabilité du "remnant scenario" comme solution au paradoxe de l'information. 2-Le scénario "trou-noir-trou-blanc" est fortement instable. Une modification minimale est proposée pour résoudre ce problème. 3-Une généralisation des quatre lois de la thermodynamique des TN est démontrée pour des cônes de lumière s'intersectant dans un espace de Minkowski. 4-On étudie des espaces conformellement plats où de telles lois acquièrent une interprétation thermodynamique standard. Le plus simple est l'espace-temps de Bertotti-Robinson, connu pour encoder la géométrie proche de l'horizon d'un TN chargé. 5-Pour peu que le bon tenseur énergie-impulsion soit identifié, les équations du champ Einstein-Cartan peuvent être retrouvées comme l'équation d'état d'un équilibre thermodynamique, comme dans le cas original de la RG. Ces résultats contribuent au débat intense sur les questions cruciales posées ci-dessusSince 1916 intriguing questions have arisen from the study of Black Holes (BH). Only some of them have been resolved. Indeed, we are faced with regimes where the yet unknown interplay between quantum theory and spacetime unveils. BH physics is a gateway to the quantum nature of gravity. My thesis has been completely devoted to this central domain of theoretical physics, with the guiding aim of understanding in the widest possible manner the debate around those questions. The process has produced original results that constitute the main core of the manuscript. 1- The maximal volume surfaces of evaporating BHs are studied. An astrophysical BH will end its life with an external planckian area $10^{-70} m^2$ hiding $10^5$ times the volume of our observable Universe. This can have consequences on the viability of the “remnant scenario” as solution to the BH information paradox. 2- The “black-hole-to-white-hole scenario” is analyzed. The model is shown to be strongly unstable, and a minimal resolutive modification is proposed. 3- A generalisation of the four laws of BH thermodynamics is proven for intersecting light cones in Minkowski spacetime. 4- Conformally flat spaces where such laws acquire the standard thermodynamical interpretation are studied. The simplest one is the Bertotti-Robinson spacetime, known to encode the near-horizon geometry of a charged BH. 5- It is shown that, if the correct energy-momentum tensor is identified, the Eintein-Cartan’s field equations can be recovered as a thermodynamical equilibrium equation of state just like in the GR original case. Such results contribute to the intense debate on the opening crucial questions
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Bhattacharyya, Anirban. "Application of effective field theory to density functional theory for finite systems." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124116299.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xv, 210 p.; also includes graphics (some col.). Includes bibliographical references (p. 205-210). Available online via OhioLINK's ETD Center
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Chenaghlou, Alireza. "Quantum corrections to the classical reflection factor of the sinh-Gordon model." Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4347/.
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This thesis studies the quantum reflection factor of the sinh-Gordon model under boundary conditions consistent with integrability. First, we review the affine Toda field theory in Chapter One. In particular, the classical and quantum integrability of the theory are reviewed on the whole line and on the half-line as well, that is, in the presence of a boundary. We next consider the sinh-Gordon model which is restricted to a half-line by boundary conditions maintaining integrability in Chapter Two. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary. The result provides a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling. In Chapter Three, quantum corrections to the classical reflection factor of the sinh-Gordon model are studied up to second order in the difference of boundary data and to one loop order in the bulk coupling. Chapter Four deals with the quantum reflection factor for the sinh-Gordon model with general boundary conditions. The model is studied under boundary conditions which are compatible with integrability and in the framework of the conventional perturbation theory generalised to the affine Toda field theory. It is found that the general form of a subset of the related quantum corrections are hypergeometric functions. Finally, we sum up this thesis in Chapter Five along with some conclusions and suggestions for further future studies.
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Weidig, Tom. "Classical and quantum aspects of topological solitons (using numerical methods)." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4277/.
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In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimize functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal- energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi- skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the Ф(^4) kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of Ф(^4) kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula.
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Frye, Christopher. "Modification to Einstein's field equations imposed by string theory and consequences for the classical tests of general relativity." Honors in the Major Thesis, University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/852.
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String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.B.S.
Bachelors
Sciences
Physics
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Stapleton, David Paul. "A technique for the analysis of the invariance identities of classical gauge field theory by means of functional equations." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185191.
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In order to obtain the equations of motion for a particle in a classical gauge field, a variational principle is considered. The theory is general in that the structural group is an arbitrary r-dimensional Lie group and the base space is an arbitrary n-dimensional psuedo-Riemannian manifold. An n + r dimensional principal fiber bundle is constructed in order to introduce the usual gauge potentials and field strengths. In addition, a set of r quantities (called "coupling parameters") which transform as the components of an adjoint type (0,1) object and also depend upon the parameter of the particle's trajectory are constructed. The gauge potentials and coupling parameters are evaluated on the identity section of the principle bundle, and the Lagrangian is assumed to be a C³ scalar function of these and of the components of the metric tensor and tangent vector on the base space. The Lagrangian is not gauge-invariant, but it is stipulated that when the arguments of the Euler-Lagrange vector (evaluated on the identity section) are replaced by their counterparts (which may be evaluated on an arbitrary section) the resulting vector must be gauge-invariant. A novel application of methods from the theory of functional equations is applied together with standard techniques inherent in the theory of differential equations to show that the arguments of the Lagrangian must occur together in certain prescribed combinations. The invariance postulates uniquely determine the Lagrangian in terms of its arguments other than the coupling parameters and r functions of the coupling parameters. The Lagrangian is shown to separate into a free-field term and an interaction term, and the functions of the coupling parameters are found to be the components of an adjoint type (0,1) quantity whose adjoint absolute derivative vanishes. This agrees with the equations of certain approaches to the Yang-Mills theory for isotopic spin particles.¹ Standard initial conditions are shown to determine a unique (local) solution to the derived equations of motion. ftn¹ The equations have the same formal structure as systems obtained in the classical limit of quantum mechanical results found by Wong (1), pp. 691-693.
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Fabis, Felix [Verfasser], and Matthias [Akademischer Betreuer] Bartelmann. "A Statistical Field Theory for Classical Particles - Foundations and Applications in Cosmological Structure Formation / Felix Fabis ; Betreuer: Matthias Bartelmann." Heidelberg : Universitätsbibliothek Heidelberg, 2015. http://d-nb.info/1180396073/34.
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Rosaler, Joshua S. "Inter-theory relations in physics : case studies from quantum mechanics and quantum field theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1fc6c67d-8c8e-4e92-a9ee-41eeae80e145.
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I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
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Nilsson, Daniel. "The Ratio of Reality : A study of the gyromagnetic ratio in theories ranging from classical mechanics to string theory." Thesis, Uppsala universitet, Teoretisk fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-448767.
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In this project a theoretical study of the so called gyromagnetic ratio was done by investigating classical mechanics, Dirac theory and string theory. The gyromagnetic ratio is a constant term appearing in the coupling between angular momentum and magnetic moment for a particle. A universality in quantum field theory claiming g = 2 regardless of spin is known to exist which also agrees with the found values (g = 2) of the Dirac and string theory. The proof of the aforementioned universality in quantum field theory was sketched in the project by showing that the W-boson Lagrangian is well behaved in the massless limit. Furthermore it is shown that the spin equations of motion for a particle is greatly reduced if g = 2 regardless of spin.I det här projektet utfördes en teoretisk studie av den så kallade gyromagnetsika kvoten genom att undersöka klassisk mekanik, Dirac-teori och strängteori. Den gyromagnetiska kvoten är en konstant term som visar sig i kopplingen mellan rörelsemängsmoment och magnetiskt moment för en partikel. I kvantfältsteori existerar en universalitet som hävdar att g = 2 oberoende av spin. Denna universalitet stämmer överens med de funna värden på g från Dirac-teori och strängtoeri. Beviset för denna universalitet testades genom ett exempel där Lagrangianen för W-bosonen i kvantfältsteori visades bete sig som förväntat när massan för partikeln tilläts gå mot noll. Vidare undersöktes rörelseekvationerna för ett system helt bestämt av dess spin. I dessa kan det visas att ett universellt värde på g oavsett spin reducerar dessa ekvationer avsevärt.
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Pêgas, Luiz Henrique Pereira. "Grupoides de Lie e o teorema de Noether na formulação lagrangiana da teoria clássica de campos." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-07112014-152249/.
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O objetivo desta tese é oferecer um arcabouço que permita a modelagem de simetrias em fibrados suaves, que possuam um bom comportamento local. Para tanto, usa-se ferramentas de grupoides de Lie e correlatas, com a finalidade de reduzir, quando possível, simetrias dadas pela ação de um grupo diferenciável, possivelmente de dimensão infinita, sobre um fibrado suave, a problemas em dimensão finita. Uma definição de invariância de uma forma diferencial, definida no espaço total de um fibrado suave, sob a ação de um grupoide de Lie, é apresentada e desenvolvida. A seguir, discute-se estas ferramentas no contexto da formulação lagrangiana da teoria clássica de campos com o objetivo de descrever, simultaneamente, simetrias internas e no espaço-tempo, de maneira unificada. Obtém-se então, nesta linguagem, alguns objetos de estudo centrais da teoria, como os teoremas de Noether e, no caso das teorias de calibre, os teoremas de acoplamento mínimo e Utiyama. Por fim, discute-se brevemente o caso de simetrias a menos de elementos de contato e divergências totais.The aim of this thesis is to provide a framework that allows the modelling of symmetries in smooth fibre bundles which have good local behaviour. For that, we use Lie groupoids and related tools in order to reduce, whenever possible, symmetries given by the action of a possibly infinite dimensional differentiable group on a smooth fibre bundle to finite dimensional problems. We give a definition of invariance of a differential form, defined on the total space of a fibre bundle, by the action of a Lie groupoid. Then, we discuss these tools in the case of a Lagrangian classical field theory to describe internal and space-time symmetries simultaneously, in a unified way. With this language, we get some central objects of the theory such as Noether\'s theorems and, in the case of gauge theories, the minimal coupling and Utiyama\'s theorems. Lastly, we briefly discuss the case of symmetries up to contact elements and a total divergence.
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Boonzaaier, Leandro. "Confined counterions surrounding a Macroion : a field theoretic approach." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17853.
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Thesis (PhD)--Stellenbosch University, 2011.ENGLISH ABSTRACT: Several experiments [1, 2, 3, 4] have shown that e ective attractive interactions exist between con ned like-charged macromolecules. Theoretical approaches have not reached consensus as to precisely what the mechanism for the attraction is, but it is agreed that comprehending the role of the counterion arrangement around macromolecules is crucial for understanding the e ective macromolecule interactions. It is generally assumed that attraction only occurs in the limit of strong electrostatic coupling and is driven by correlation e ects that are neglible in a mean- eld approach, which is valid in the weak-coupling limit. However, in some experimental situations attraction occurs even in the limit of weak-coupling. We consider a eld-theoretic approach that includes uctuations to study the Coulomb interactions of con ned counterions with a single exible charged spherical macromolecule that can expand or collapse uniformly by changing its radius. We show how the linearised eld-theory (valid in the weak-coupling limit) is mapped onto the square-well potential of Quantum Mechanics. The con nement leads to bound states being present in the spectrum at all times. Bound states are non-perturbative and we investigate the role they play in the physics of the system. Some of the e ects are rather counter-intuitive. Firstly, upon expanding the macromolecule in a xed con nement volume, the uctuation part of the free energy favours a decrease in the free energy. Secondly, upon increasing the temperature to high but nite values, the uctuation contribution does not dominate the free energy as would be expected. The mathematical origins of these e ects are dicussed in detail and as part of the analysis we introduce a novel regularisation scheme for computing the functional determinant arising in the model considered where the cut-o is speci ed unambiguously in terms of physical parameters.
AFRIKAANSE OPSOMMING: Verskeie eksperimente [1, 2, 3, 4] toon dat makro-ione met gelyksoortige ladings, in `n eindige volume, `n e ektiewe aantrekkende krag ondervind. Alhoewel daar nog geen konsensus oor die presiese meganisme vir die aantrekking bereik is nie, is dit duidelik dat die rol van \counter-ion" rangskikking rondom die makro-ione belangrik is om die e ektiewe wisselwerkings te verstaan. Dit word algemeen aanvaar dat die aantrekkende krag slegs in die limiet van sterk elektrostatiese koppeling plaasvind en dat dit `n gevolg van \counter-ion" korrelasies is wat weglaatbaar is in `n gemiddelde veld benadering, wat geldig is in die limiet van swak elektrostatiese koppeling. Daar bestaan egter eksperimentele situasies waar die aantrekking in die limiet van swak elektrostatiese koppeling waargeneem word. Ons bestudeer die Coulomb wisselwerking tussen \counter-ions" en `n enkele rekbare sferiese makro-ioon vanuit `n veld-teoretiese beskouing wat uktuasies in ag neem. Die sferiese makro-ioon kan vergroot of verklein deur sy radius uniform te verander. Ons toon aan dat die gelineariseerde veldeteorie (geldig in die limiet van swak elektrostatiese koppeling) op die eindige-diepte put Kwantummeganiese model afgebeeld kan word. Die eindige volume van die sisteem het tot gevolg dat daar altyd gebonde toestande in die spektrum voorkom. Gebonde toestande is `n suiwer nie-steuringsteoretiese e ek en ons ondersoek die rol wat dit speel in die sika van die sisteem. Die teenwoordigheid van die gebonde toestande in die spektrum het `n paar teen-intuitiewe e ekte tot gevolg. Eerstens word die vrye energie verlaag soos die makro-ioon in `n eindige volume vergroot. Tweedens oorheers die uktuasie bydrae nie die vrye energie met toenemende temperatuur soos verwag sou word nie. Ons bespreek die wiskundige oorsprong van hierdie e ekte. As deel van die analise ontwikkel ons `n nuwe regulariseringstegniek vir die berekening van funksionaalintegrale waar die regulariseringsparameter ondubbelsinnig in terme van siese hoeveelhede uitgedruk kan word.
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Vieira, Lucas Elias. "Campos escalares aplicados em cosmologia." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8819.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we study topological defects in classical field theory aiming applications in cosmology. Topological and non-topological solutions were investigated in two dimensions, where we also analyzed the stability of some of these. We consider models of one and two real scalar fields, whose solutions were obtained via quadrature, BPS and orbit methods. The stability of these solutions also were investigated in some cases. In order to apply scalar field theory in cosmology, we revisit some topics of general relativity, such that the principle of equivalence, Einstein's field equations and Schwarzschild's solution for Einstein's equation. We also present some topics in cosmology, relevant to the present work, such that the cosmological principle, Hubble's law and cosmological inflation. We discuss the solutions of the Einstein's equations in the FRW metric in the so-called Hot Big Bang model-the universe composed of matter and radiation. In order to solve some problems of initial conditions of the universe, we introduce the inflationary theory, which supposes that the primordial universe was underwent an accelerated expansion guided by a scalar field. In sequence, we introduce the standard cosmological model, which states that the universe is in accelerated expansion driving by a cosmological constant, named dark energy, which constitutes about seventy percent of the universe energy. Finally, we present a first order formalism for cosmology and discuss two model describing the standard and tachyonics dynamics for scalar field that represent the dark energy.
Neste trabalho foram abordadas soluções do tipo defeitos topológicos em teoria clássica de campos. Foram investigadas soluções topológicas e não topológicas em duas dimensões, onde também analisamos a estabilidade de algumas destas. Consideramos modelos de um e dois campos escalares reais, onde utilizamos os métodos de quadratura, BPS e das órbitas para obter soluções. Com o intuito de aplicar a teoria de campos escalares em cosmologia, introduzimos a teoria da relatividade geral, falando sobre o princípio da equivalência, equações de campo de Einstein e solução de Schwarzschild para as equações de Einstein. Abordamos alguns tópicos em cosmologia, onde enunciamos o princípio cosmológico, lei de Hubble e inflação cosmológica. Resolvemos as equações de Einstein na métrica FRW considerando o universo composto de matéria e radiação denominado modelo Big Bang quente. Com o objetivo de resolver alguns problemas de condições iniciais do universo, introduzimos a teoria inflacionária, a qual propõe que o universo primordial sofreu uma expansão acelerada guiada por um campo escalar. Após mostrar como a teoria da inflação corrige tais problemas, apresentamos o modelo cosmológico padrão, o qual afirma que o universo está em expansão acelerada e utiliza uma constante cosmológica como guia da expansão, tal constante neste cenário representa a denominada energia escura que compõe aproximadamente setenta por cento do universo. Finalmente, nós apresentamos o formalismo de primeira ordem para cosmologia e discutimos dois modelos descrevendo dinâmicas padrão e taquiônica para o campo escalar, representando a energia escura.
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Caberlim, Cristiane Candido Luz. "Letramento probabilístico no Ensino Médio: um estudo de invariantes operatórios mobilizados por alunos." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11028.
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Previous issue date: 2015-03-18Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The Subject in which this research was developed is the development of the learning process of the probability. For this, we search the subjects of official documents and researches that addressed the teaching or the learning of probability, and we realize its growing withing mathematics education s field, confirming our hypotheses about the relevance of develop a research in this subject. In this context, we formulate our goal that s diagnose invariant operative mobilized by students. In situation of troubleshooting, and to seek elements that allowing a proposal for a concept of building model (learning evolution model). The work developed trying to relate the identified operative invariant with the elements of probabilistic literacy when learning of probability mobilizes elements of geometric probability, articulating the classical approach and the frequentist approach to probability. To achieve the goal, we formulated the following research question: Which literacy probabilistic elements identified in mobilizing operative invariants by third grade of high school students to solve problems that articulate the classical approach and the frequentist concepto f probability? Claving to answer this question, We Will use the theory of conceptual fields linking it with the principles of probabilistic literacy. As a research methodology chose the case study. Our sequence comprises three adapted teaching situations developed earlier research, in our research group, called A Bernoulli urn , B Pixels urn and C Franc-Carreau game and these situations were applied to a group of student volunteers attending the third high school of a private school in São Paulo. The analysis of the protocols built allowed us to identify students mobilized operative invariants allowing estimate the probability, articulating the classical approach and frequentist, confirming development of probabilistic assumptions literacy. Reported proportions via an own speech, transiting the concrete domains and pseudo-concrete. No student has achieved the full probabilistic literacy, that supposed to problem solving in the abstract domain, under the proposed scheme for a process of abstraction to be followed during learning
O tema no qual esta pesquisa se desenvolveu é o desenvolvimento do processo de aprendizagem da probabilidade. Para tal, buscamos primeiramente os conteúdos de documentos oficiais e pesquisas que abordaram o ensino ou a aprendizagem da probabilidade, e percebemos o seu crescimento dentro do campo da Educação Matemática, confirmando nossas hipóteses sobre a relevância de se desenvolver uma pesquisa nesse tema. Neste contexto, formulamos nosso objetivo que é diagnosticar invariantes operatórios mobilizados pelos alunos em situação de resolução de problemas, para que busquemos elementos que permitam uma proposta de modelo de construção de conceito (modelo de evolução de aprendizagem). O trabalho se desenvolveu buscando relacionar os invariantes operatórios identificados com os elementos do letramento probabilístico quando a aprendizagem da probabilidade mobiliza elementos da probabilidade geométrica, articulando o enfoque clássico e o enfoque frequentista da probabilidade. Para alcançarmos tal objetivo, formulamos a seguinte questão de pesquisa: Que elementos do letramento probabilístico identificamos na mobilização de invariantes operatórios por alunos do 3º ano do Ensino Médio ao resolver problemas que articulam o enfoque clássico e frequentista do conceito de probabilidade? Almejando responder a essa questão, utilizaremos a Teoria dos Campos Conceituais articulando-a com os princípios do letramento probabilístico. Como metodologia de pesquisa escolhemos o estudo de caso. Nossa sequência é composta por três situações didáticas adaptadas de pesquisa anterior desenvolvida em nosso grupo de pesquisa, denominadas A-Urna de Bernoulli , B-Urna de Pixels e C-O jogo Franc-Carreau e estas situações foram aplicadas a um grupo de alunos voluntários, cursando o terceiro ano do Ensino Médio de uma escola da rede privada da cidade de São Paulo. A análise dos protocolos construídos nos permitiu identificar que os alunos mobilizaram invariantes operatórios que permitiam estimar a probabilidade, articulando o enfoque clássico e frequentista, confirmando hipótese de desenvolvimento do letramento probabilístico. Descreveram proporções e por meio de um discurso próprio, transitando pelos domínios concreto e pseudoconcreto. Nenhum aluno atingiu o letramento probabilístico pleno, que supunha a resolução de problemas no domínio abstrato, segundo o esquema proposto para um processo de abstração a ser percorrido durante a aprendizagem
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Costa, Bruno Tadeu. "Grupoides de Lie e o teorema de Noether em teoria de campos no âmbito hamiltoniano." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-03102016-175645/.
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Neste trabalho, abordamos o conceito de simetria em teoria de campos, no âmbito hamiltoniano mais precisamente, sua relação com leis de conservação, conforme estabelecida pelo(s) teorema(s) de Noether. Propomos uma visão alternativa àquela normalmente usada na literatura, baseada na substituição de grupos e álgebras de Lie por grupoides e algebroides de Lie. Tradicionalmente, dado um fibrado E de configuração sobre o espaço-tempo M (cujas seções são os campos do modelo sob investigação), simetrias são implementadas pela ação de um grupo de automorfismos de E, ou seja, um subgrupo de Aut(E), no espaço Γ (E) das seções de E, exigindo-se que o funcional ação S seja invariante sob tal ação: neste caso, quando o pertinente subgrupo for de dimensão infinita, surgem graves dificuldades quando queremos tratar de questões de análise e de geometria com rigor matemático. A vantagem principal desta abordagem alternativa provém do fato de que, embora o grupo Aut(E) e, tipicamente, os subgrupos relevantes, assim como o espaço Γ (E), sejam de dimensão infinita, a sua ação é induzida por uma ação de um grupoide de Lie no fibrado pertinente, a qual envolve apenas variedades de dimensão finita e portanto não há qualquer dúvida em relação a questões tais como qual seria a topologia ou estrutura de variedade subjacente ou em qual sentido essa ação deve ser suave. Formulamos o teorema de Noether neste contexto, baseado em uma nova versão da construção da aplicação momento que a cada gerador de simetrias que associa uma (n - 1)-forma sobre J*E cujo pull-back com uma seção de J* E, que é solução das equações de movimento, produz uma (n - 1)-forma sobre o espaço-tempo, a famosa corrente de Noether, que é conservada, ou seja, fechadaIn this thesis, we deal with the concept of symmetry in field theory, in the covariant hamiltonian approach more precisely, its relation with conservation laws, as established by Noethers theorem(s). We propose an alternative view to that normally used in the literature, based on replacing Lie groups and algebras by Lie groupoids and algebroids. Traditionally, given a configuration bundle E over space-time M (whose sections are the fields of the model under investigation), symmetries are implemented by the action of a group of automorphisms of E, i.e., a subgroup of Aut(E), on the space Γ (E) of sections of E, requiring the action functional S to be invariant under that action: in this case, when the pertinent subgroup has infinite dimension, serious difficulties arise when we want to deal with analytical and geometrical questions with mathematical rigor. The main advantage of this alternative approach comes from the fact that, although the group Aut(E) and, typically, the relevant subgroups, as well as the space Γ (E), are infinite-dimensional, its action is induced by the action of a Lie groupoid in the pertinent bundle, which involves only finite-dimentional manifolds and therefore there is no doubt about questions such as what should be the topology or the underlying manifold structure or in what sense this action should be smooth. We formulate the Noethers theorem in this context, based on a new version of the construction of the momentum map that associates a (n - 1)-form on J*E to each symmetries generator whose pull-back with a section of J*E, that is solution of the equations of motion, produces a (n - 1)-form on the space-time, the famous Noether current, that is conserved, i.e., closed
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Bär, Christian, and Nicolas Ginoux. "Classical and quantum fields on Lorentzian manifolds." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5997/.
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We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
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Knapman, Alan. "Classical and quantum fields in brane worlds." Thesis, University of London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407818.
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Gundlach, C. "Classical and quantum scalar fields in cosmology." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240140.
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Haberichter, Mareike Katharina. "Classically spinning and isospinning non-linear σ-model solitons." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/classically-spinning-and-isospinning-nonlinear-sigmamodel-solitons(59f1d53d-0de7-4938-ad02-85ac57f6003f).html.
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We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1) and (3+1) dimensions and Hopf soliton solutions in (3 +1) dimensions. For example, such soliton types can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems, can model spin and isospin states of nuclei and may be candidates to model glueball configurations in QCD.Unlike previous work, we do not impose any spatial symmetries on the isospinning soliton configurations and we explicitly allow the isospinning solitons to deform and break the symmetries of the static configurations. It turns out that soliton deformations clearly cannot be ignored. Depending on the topological model under investigation they can give rise to new types of instabilities, can result in new solution types which are unstable for vanishing isospin, can rearrange the spectrum of minimal energy solutions and can allow for transitions between different minimal-energy solutions in a given topological sector. Evidently, our numerical results on classically isospinning, arbitrarily deforming solitons are relevant for the quantization of classical soliton solutions.
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Söderberg, Alexander. "Symmetries of the Point Particle." Thesis, Uppsala universitet, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-227338.
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We study point particles to illustrate the various symmetries such as the Poincaré group and its non-relativistic version. In order to find the Noether charges and the Noether currents, which are conserved under physical symmetries, we study Noether’s theorem. We describe the Pauli-Lubanski spin vector, which is invariant under the Poincaré group and describes the spin of a particle in field theory. By promoting the Pauli-Lubanski spin vector to an operator in the quantized theory we will see that it describes the spin of a particle. Moreover, we find an action for a smooth spinning bosonic particle by compactifying one string dimension together with one embedding dimension. As with the Pauli-Lubanski spin vector, we need to quantize this action to confirm that it is the action for a smooth spinning particle.Vi studerar punktpartiklar för att illustrera olika symemtrier som t.ex. Poincaré gruppen och dess icke-relativistiska version. För att hitta de Noether laddningar och Noether strömmar, vilka är bevarade under symmetrier, studerar vi Noether’s sats. Vi beskriver Pauli-Lubanksi spin vektorn, vilken har en invarians under Poincaré gruppen och beskriver spin hos en partikel i fältteori. Genom att låta Pauli-Lubanski spin vektorn agera på ett tillstånd i kvantfältteori ser vi att den beskriver spin hos en partikel. Dessutom finner vi en verkan för en spinnande partikel genom att kompaktifiera en bosonisk sträng dimension tillsammans med en inbäddad dimension. Som med Pauli-Lubanski spin vektorn, kvantiserar vi denna verkan för att bekräfta att det är en verkan för en spinnande partikel.
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Santos, Joao Rafael Lucio dos. "Tópicos em defeitos deformados e o movimento Browniano." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/5748.
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Previous issue date: 2013-11-20Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The non-linear science is a central topic covering several investigation areas, such as biology, chemistry, mathematics and physics. In the first part of this thesis, we studied the non-linearity in the scope of classical field theory. The discussions are based on static solutions in (1, 1) space-time dimensions, and they are focused on kinks and lumps defects. In the related procedures, we show several techniques which allowed us to determine new models with their respective analytical solutions. The main mathematical tool to obtain these results is the so called deformation method, which was also an essential piece in the construction of a new extension method. This method presents the determination of new two scalar fields models from the coupling between two one scalar field systems. The method was analyzed carefully, as well as the linear stability, the zero modes, the total energy and the superpotentials, related with the new families of potentials. Furthermore, in the second part we presented the basics concepts about the Brownian Motion, where we analised the features of the solution of the Langevin Equation, and we also introduced a path integral approach to this problem in a quantum field theory way.
A ciência não-linear é tema central de diversas linhas de investigação, cobrindo áreas como a biologia, a física, a matemática e a química. Nossa primeira vertente de trabalho nesta tese, consiste no estudo de não-linearidades via abordagem de teoria clássica de campos. As discussões estão baseadas em soluções estáticas em (1, 1) dimensões, com destaque para o chamados defeitos tipo kink e lump. Nos procedimentos relatados, discorremos a respeito de diversas técnicas para a determinação de novos modelos com suas respectivas soluções analíticas. Um ferramental fundamental para a obtenção desses resultados é o chamado método de deformação, o qual também foi parte essencial para a criação de um método de extensão de modelos, onde visamos a construção de modelos de dois campos reais a partir do acoplamento entre dois modelos de um campo. Tal método também foi exposto em detalhes, bem como as análises sobre estabilidade linear, cálculo de modos zeros, determinação da energia total e dos superpotenciais, relativos às novas famílias de potenciais. Já a segunda linha de pesquisa, refere-se aos conceitos básicos do movimento browniano, onde analisamos as propriedades da solução da equação de Langevin, e na introdução de uma abordagem via integrais de trajetória para descrevê-lo nos moldes de teoria de quântica de campos.
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Lechner, Gandalf. "On the construction of quantum field theories with factorizing S-matrices." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/lechner.
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Lanza, Victor. "The Classical Approach to Capital Accumulation : Classical Theory of Economic Growth." Thesis, Umeå universitet, Nationalekonomi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-60777.
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Britnell, John R. "Cycle index methods for matrix groups over finite fields." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275602.
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Hilgenböcker, Kirsten. "Wolbachia's role in classical speciation theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2009. http://dx.doi.org/10.18452/16020.
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Wolbachien sind intrazeklluläre Bakterien die zahlreiche Arthropodenarten infizieren. Sie induzieren häufig eine zytoplasmatische Paarungsinkompatibilität die postzygotische Isolation zwischen unterschiedlich infizierten Individuen der gleichen Wirtsart verursacht, weswegen Wolbachien Beachtung als mögliche Katalysatoren von Artbildungsprozessen gefunden haben. Vorherige Arbeiten zur Artbildung untersuchten meist entweder Wolbachia-induzierte oder die klassischen, genetischen postzygotischen Isolationsmechanismen. Normalerweise sollte es aber der Fall sein dass beide Mechanism gleichzeitig auftreten. In dieser Arbeit führen wir Untersuchungen zur Rolle der Wolbachien in der Artbildung fort indem wir die Interaktionen von Wolbachia-induzierten und genetischen Inkompatibilitäten analysieren. Wir werden zeigen dass Wolbachien einen starken Einfluss auf genetisch-basierte Artbildungsprozesse haben. Insbesondere können sich die Mechanism bei gleichzeitigem Auftreten katalysieren. Außerdem werden wir zeigen dass Wolbachia Artbildungsprozesse unter allgemeineren Bedingungen beeinflussen kann als vorherige Studien suggerierten. Da die Rolle der Wolbachien in der Artbildung stark von deren Verbreitung abhängt, werden wir desweiteren eine statistische Metaanalyse von bestehenden Daten zu Infektionsfrequenzen präsentieren. Aufgrund der Methoden der Datenerhebung ist es sehr wahrscheinlich, dass der wirkliche Anteil der infizierten Arten mit 20% deutlich unterschätzt wird. Unsere Analyse bestätigt dies und zeigt dass viel wahrscheinlicher circa zwei Drittel aller Arten infiziert sind. Unsere Resultate der klassischen Artbildungstheorie kombiniert mit denen der statistischen Analyse zu Infektionsfrequenzen von Wolbachia implizieren dass Wolbachien als allgemeine Faktoren in der Evolution von Arthropoden anzusehen sind.Wolbachia are intracellular bacteria that commonly infect arthropod species. Since they often induce a cytoplasmic mating incompatibility (CI) in their hosts that acts as a postzygotic isolating mechanism between differently infected individuals of one species, Wolbachia have received attention as a potential promoter of arthropod speciation processes. Previous studies on speciation focused on either Wolbachia-induced or the classical nuclear-based postzygotic isolating mechanism. However, it should usually be the case that both co-occur. This thesis continues investigations on Wolbachia''s role in speciation by analyzing interactions of Wolbachia-induced CI and nuclear incompatibility (NI) caused by genetic differentiation. We will show that Wolbachia have strong impact on nuclear-based speciation processes. In particular, synergy effects can occur when both isolating mechanisms act simultaneously. Furthermore, we show that Wolbachia can influence speciation processes under more general conditions than previous studies on Wolbachia''s role in speciation suggested. Since the actual role of Wolbachia in arthropod speciation will strongly depend on their abundance, we present a statistical meta-analysis of published data on Wolbachia infection frequencies. Due to the sampling methods applied in studies on Wolbachia infection frequencies, it is likely that current estimates of 20% infected species are underestimates. This is supported by our analysis and we show that more likely about two-thirds of species are infected. Combining both results, this thesis provides strong evidence for Wolbachia being a very general factor in arthropod speciation processes.
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Kryvohuz, Maksym. "Quantum-classical correspondence in response theory." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43759.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2008.Includes bibliographical references (p. 113-118).
In this thesis, theoretical analysis of correspondence between classical and quantum dynamics is studied in the context of response theory. Thesis discusses the mathematical origin of time-divergence of classical response functions and explains the failure of classical dynamic perturbation theory. The method of phase space quantization and the method of semiclassical corrections are introduced to converge semiclassical expansion of quantum response function. The analysis of classical limit of quantum response functions in the Weyl-Wigner representation reveals the source of time-divergence of classical response functions and shows the non-commutativity of the limits of long time and small Planck constant. The classical response function is obtained as the leading term of the h-expansion of the Weyl-Wigner phase space representation and increases without bound at long times as a result of ignoring divergent higher order contributions. Systematical inclusion of higher order contributions improves the accuracy of the h expansion at finite times. The time interval for the quantum-classical correspondence is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity. The effects of dissipation on the correspondence between classical and quantum response functions are studied. The quantum-classical correspondence is shown to improve if coupling to the environment is introduced. In the last part of thesis the effect of quantum chaos on photon echo-signal of two-electronic state molecular systems is studied. The temporal photon echo signal is shown to reveal key information about the nuclear dynamics in the excited electronic state surface.
(cont.) The suppression of echo signals is demonstrated as a signature of level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state.
by Maksym Kryvohuz.
Ph.D.
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Hanif, Sohail. "A theory of early classical Ḥanafism." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:64a8d79a-123a-493c-a864-fb2c48830e7e.
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Fiqh, literally 'deep understanding', is the science of religious law in Islam. What does it mean for an Islamic jurist to 'do fiqh'? And how does an engagement with fiqh guide a jurist to produce statements of law for particular social contexts? These are perennial questions in the field of Islamic legal studies. The current thesis offers an answer to these questions from the viewpoint of jurists from the early classical Ḥanafī tradition of Central Asia. The thesis starts with an examination of Central-Asian Ḥanafī works of legal theory to extract the underlying epistemological foundations of this legal tradition. The remainder of the thesis presents a series of investigations into a leading work of legal commentary - the Hidāyah of Burhān al-Dīn 'Alī ibn Abī Bakr al-Marghīnānī (d. 593/1197) - to assess how these epistemological foundations inform the work. These investigations range from a study of the processes by which the legal cases commented on in the work were seen to be authoritative, to a study of the use of rational arguments, dialectical sequences and juristic disagreement in exploring and expositing cases of the law. The thesis also studies points of theory employed in the commentary that reveal how social context was seen to impact on the production of law. The study concludes by suggesting a general theory of Ḥanafī jurisprudence, explaining what it means to 'do fiqh' - presented as a particular form of engagement with the legal cases transmitted from the teaching circle of Abū Ḥanīfah (d. 150/767), the school's eponym - and how this fiqh engagement with Ḥanafī precedent informed the production of legal statements tailored to specific contexts - by the application of a particular filter of legal mechanisms, each of which reflects an understanding of the overarching principle of 'necessity' (ḍarūrah). The study presents a uniquely Ḥanafī legal epistemology which is underpinned by particular notions of authority, rationality and tradition.
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Favaro, Alberto. "Recent advances in classical electromagnetic theory." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/10482.
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The early Sections of the present Thesis utilise a metric-free and connection-free approach so as derive the foundations of classical electrodynamics. More specifically, following a tradition established by Kottler [65], Cartan [14] and van Dantzig [137], Maxwell's theory is introduced without making reference to a notion of distance or parallel transport. With very few exceptions, the relevant concepts are derived from first principles. Indeed, Maxwell's theory is constructed starting from three experimentally justified axioms: (i) electric charge is conserved, (ii) the force acting on a test charge due to the electromagnetic field is the standard Lorentz one, (iii) magnetic flux is conserved. To be precise, a strictly deductive approach requires that three further postulates are introduced, as explained in the manual [41] by Hehl and Obukhov. Nevertheless, a shortened formalism is observed to be adequate for the purpose of this work. In nearly all cases, the electromagnetic medium is demanded to be local and linear. Moreover, the propagation of light is studied in the approximate geometrical optics regime. Lindell's astute derivation of the dispersion equation [80] is reformulated in the widespread mathematical language of tensor indices. The method devised in Ref. [80] is integrated with the analysis due to Dahl [16] of the space encompassing the physically viable polarisations. As a result, the geometry associated with the dispersion equation is investigated with considerable rigour. From the literature it is known that, to a great extent, the notion of distance can be viewed as a by-product of Maxwell's theory. In fact, imposing that the constitutive law is electric-magnetic reciprocal and skewon-free determines, albeit non-uniquely, a Lorentzian metric. A novel proof of this statement is examined. In addition, the unimodular forerunner of electric-magnetic reciprocity, defined in earlier works by Lindell [79] and Perlick [112], is shown to preserve the energy-momentum tensor.
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Heiderich, Florian. "Galois Theory of Module Fields." Doctoral thesis, Universitat de Barcelona, 2010. http://hdl.handle.net/10803/674.
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This thesis is about Galois theory.The development of a Galois theory for differential equations analogous to the classical Galois theory for polynomial equations was already an aim of S. Lie in the 19th century. The first step in this direction was the development of a Galois theory for linear differential equations due to E. Picard and E. Vessiot. Later, B.H. Matzat and M. van der Put created a theory for iterative differential equations in positive characteristic. H. Umemura constructed a Galois theory for algebraic differential equations in characteristic zero.
There also exist analog theories for difference equations, starting with a theory for linear difference equations till the one due to S. Morikawa and H. Umemura for algebraic difference equations.
M. Takeuchi, K. Amano and A. Masuoka unified Galois theories for linear differential and linear difference equations using the language of module algebras.
This thesis has two goals. The first is the development of a more general Galois theory that combines the capacity of the theories of H. Umemura and S. Morikawa, which allow the treatment of field extensions of big generality, with the advantage of the formulation of K. Amano and A. Masuoka, which unifies structures like derivations and automorphisms. The second goal is the removal of the restriction to fields of characteristic zero from the theories of H. Umemura and S. Morikawa.
KEY WORDS: Galois Theory, Differential Equation, Difference Equation, Module Algebra
Esta tesis se desarrolla en torno a la teoría de Galois.
El desarrollo de una teoría de Galois para ecuaciones diferenciales análoga a la de ecuaciones polinomiales fue ya un objetivo de S. Lie en el siglo XIX. El primer paso en esta dirección fue el desarrollo de una teoría de Galois para ecuaciones diferenciales lineales, debido a E. Picard y E. Vessiot. Después B.H. Matzat y M. van der Put crearon una teoría para ecuaciones diferenciales iterativas lineales en característica positiva. H. Umemura elaboró una teoría de Galois para ecuaciones diferenciales algebraicas en característica cero.
Existen teorías análogas para ecuaciones en diferencias, empezando con una teoría de Galois para ecuaciones en diferencias lineales, hasta la de S. Morikawa y H. Umemura para ecuaciones en diferencias algebraicas.
M. Takeuchi, K. Amano y A. Masuoka unificaron las teorías de Galois para ecuaciones diferenciales lineales y para ecuaciones lineales en diferencias usando el lenguaje de módulo álgebras.
Esta tesis tiene dos objetivos principales. El primero es el desarrollo de una teoría de Galois más general que combine la capacidad de las teorías de H. Umemura y S. Morikawa, que permite tratar extensiones de cuerpos de gran generalidad, con la ventaja de la formulación de K. Amano y A. Masuoka que unifica estructuras como las derivaciones y los automorfismos. El segundo objetivo es el de eliminar la restricción a cuerpos de característica cero de las teorías de H. Umemura y S. Morikawa.
PALABRAS CLAVE: Teoría de Galois, Ecuación diferencial, Ecuación en diferencias, Módulo álgebras
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Mackman, Stephen William. "Gauge fields and quantum theory." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5183/.
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This thesis investigates the problems within quantum mechanics for the Bohm model caused by Lorentz invariance and the existence of photons. A model describing the electromagnetic interactions of fermions is produced which does not use photons and avoids these problems. It is then shown how these techniques can be extended to linearised gravitational interactions. Finally semi-classical gravity and the possibility of gravitationally induced collapse are considered. In the first part of the thesis two modifications to the Bohm model are proposed. One takes account of Lorentz invariance, and the other is capable of describing photons. The main part of the thesis is devoted to describing interactions in a way which does not need extra gauge particles, and so is in the same spirit as the Bohm model. Electromagnetic interactions are formed using a 4-potential operator which is calculated directly, without imposing commutation relations on the 4-potential. This leads to an expression for the 4-potential in terms of the Dirac field, and results in there being no photon states. There are various ways of constructing the theory and the scattering matrix of standard QED is compared to the scattering matrix of the version which appears to be most similar. Considering only the matrix elements between fermion states, they are found to be in agreement at the order e(^2), but disagree at the order e(^4). It follows that this model, which otherwise appears to be a self consistent theory of QED, cannot agree with experiment. The same techniques can be used to quantise General Relativity when it is linearised about the Minkowski metric. The metric operator is calculated in terms of the Dirac field. The interaction is similar to that of electrodynamics, being of order 4 in the Dirac field. Finally issues relating to gravitational collapse are discussed.