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1
Fu, Guanxing. "Maximum Principle for Reflected BSPDE and Mean Field Game Theory with Applications." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19248.
Анотація:
Diese Arbeit behandelt zwei Gebiete: stochastische partielle Rückwerts-Differentialgleichungen (BSPDEs) und Mean-Field-Games (MFGs).
Im ersten Teil wird über eine stochastische Variante der De Giorgischen Iteration ein Maximumprinzip für quasilineare reflektierte BSPDEs (RBSPDEs) auf allgemeinen Gebieten bewiesen. Als Folgerung erhalten wir ein Maximumprinzip für RBSPDEs auf beschränkten, sowie für BSPDEs auf allgemeinen Gebieten. Abschließend wird das lokale Verhalten schwacher Lösungen untersucht.
Im zweiten Teil zeigen wir zunächst die Existenz von Gleichgewichten in MFGs mit singulärer Kontrolle. Wir beweisen, dass die Lösung eines MFG ohne Endkosten und ohne Kosten in der singulären Kontrolle durch die Lösungen eines MFGs mit strikt regulären Kontrollen approximiert werden kann. Die vorgelegten Existenz- und Approximationsresultat basieren entscheidend auf der Wahl der Storokhod M1 Topologie auf dem Raum der Càdlàg-Funktion.
Anschließend betrachten wir ein MFG optimaler Portfolioliquidierung unter asymmetrischer Information. Die Lösung des MFG charakterisieren wir über eine stochastische Vorwärts-Rückwärts-Differentialgleichung (FBSDE) mit singulärer Endbedingung der Rückwärtsgleichung oder alternativ über eine FBSDE mit endlicher Endbedingung, jedoch singulärem Treiber. Wir geben ein Fixpunktargument, um die Existenz und Eindeutigkeit einer Kurzzeitlösung in einem gewichteten Funktionenraum zu zeigen. Dies ermöglicht es, das ursprüngliche MFG mit entsprechenden MFGs ohne Zustandsendbedinung zu approximieren.
Der zweite Teil wird abgeschlossen mit einem Leader-Follower-MFG mit Zustandsendbedingung im Kontext optimaler Portfolioliquidierung bei hierarchischer
Agentenstruktur. Wir zeigen, dass das Problem beider Spielertypen auf singuläre FBSDEs zurückgeführt werden kann, welche mit ähnlichen Methoden wie im vorangegangen Abschnitt behandelt werden können.The thesis is concerned with two topics: backward stochastic partial differential equations and mean filed games. In the first part, we establish a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs) on a general domain by using a stochastic version of De Giorgi’s iteration. The maximum principle for RBSPDEs on a bounded domain and the maximum principle for BSPDEs on a general domain are obtained as byproducts. Finally, the local behavior of the weak solutions is considered. In the second part, we first establish the existence of equilibria to mean field games (MFGs) with singular controls. We also prove that the solutions to MFGs with no terminal cost and no cost from singular controls can be approximated by the solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of càdlàg functions. Subsequently, we consider an MFG of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward backward stochastic differential equation (FBSDE) with possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with finite terminal value, yet singular driver. We apply the fixed point argument to prove the existence and uniqueness on a short time horizon in a weighted space. Our existence and uniqueness result allows to prove that our MFG can be approximated by a sequence of MFGs without state constraint. The final result of the second part is a leader follower MFG with terminal constraint arising from optimal portfolio liquidation between hierarchical agents. We show the problems for both follower and leader reduce to the solvability of singular FBSDEs, which can be solved by a modified approach of the previous result.
2
Patrascu, A. T. "The universal coefficient theorem and quantum field theory." Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1476590/.
Анотація:
During the end of the 1950's Alexander Grothendieck observed the importance of the coefficient groups in cohomology. Three decades later, he presented his ``Esquisse d'un Programme" to the main french funding body. This program also included the use of different coefficient groups in the definition of various (co)homologies. His proposal was rejected. Another three decades later, in the 21st century, his research proposal is considered one of the most inspiring and important collection of ideas in pure mathematics. His ideas brought together algebraic topology, geometry, Galois theory, etc. becoming the origin for several new branches of mathematics. Today, less than one year after his death, Grothendieck is considered one of the most influential mathematicians worldwide. His ideas were important for the proofs of some of the most remarkable mathematical problems like the Weil Conjectures, Mordell Conjectures and the solution of Fermat's last theorem. Grothendieck's dessins d'enfant have been used in mathematical physics in various domains. Seiberg-Witten curves, N=1 and N=2 gauge theories and matrix models are a few examples where his insights are relevant. In this thesis I try to connect the idea of cohomology with coefficients in various sheaves to some areas of modern research in physics. The applications are manifold: the universal coefficient theorem presents connections to the topological genus expansion invented by 't Hooft and applied to quantum chromodynamics (QCD) and string theory, but also to strongly coupled electronic systems or condensed matter physics. It also appears to give a more intuitive explanation for topological recursion formulas and the holomorphic anomaly equations. The counting of BPS states may also profit from this new perspective. Indeed, the merging of cohomology classes when a change in coefficient groups is implemented may be related to the wall-crossing formulas and the phenomenon of decay or coupling of BPS states while crossing stability walls. The $Ext$ groups appearing in universal coefficient theorems may be regarded as obstructions characterizing the phenomena occurring when BPS stability walls are being crossed. Another important aspect is the existence of dualities. These are the non-perturbative analogue of symmetry transformations. Until now, they were discovered more by accident or by educated guesswork. I show in this thesis that there exists an underlying structure to the dualities, a structure that connects them the number fields used as coefficients in (co)homologies. This observation makes a nontrivial connection between number theory and physics.
3
Lessa, Andre Paniago. "Supersimetria em física de partículas." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278488.
Анотація:
Orientador: Orlando Luis Goulart PeresDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
Made available in DSpace on 2018-08-08T13:51:02Z (GMT). No. of bitstreams: 1 Lessa_AndrePaniago_M.pdf: 1406320 bytes, checksum: ef9057a3046500f72b58ec6a9a5e266f (MD5) Previous issue date: 2007
Resumo: O modelo padrão das partículas elementares, baseado na invariância de Lorentz e na simetria de gauge SU(3)c Ä SU(2)L Ä U(1)Y, foi confirmado por todos os testes experimentais até o momento. No entanto, nada nos garante que é este o modelo final das interações fundamentais. Problemas teóricos como a hierarquia, o número de gerações de partículas e a assimetria bariônica e alguns dados experimentais (neutrinos massivos, matéria e energia escura) sugerem a necessidade de física além do Modelo Padrão (SM). Alguns destes problemas são resolvidos em uma importante classe de modelos, que assumem a existência de simetrias espaciais adicionais, chamada de supersimetria. A proposta deste projeto é estudar a idéia de supersimetria e sua possível relevância para a física além do Modelo Padrão. Para entendermos o princípio da supersimetria, iremos construir o Modelo Padrão Supersimétrico Mínimo (MSSM) e apresentar algumas de suas conseqüências fenomenológicas. Também serão apresentados os modelos mSUGRA e mGMSB, assim como algumas de suas principais características. Em Anexo apresentaremos algumas informações complementares, além de um trabalho desenvolvido em paralelo com o projeto de Mestrado
Abstract: The standard model of elementary particles, based in Lorentz invariance and in the gauge symmetries SU(3)c Ä SU(2)L Ä U(1)Y, was confirmed by all experimental data so far. However there is no evidence that it is the final theory of fundamental interactions. In fact, several theoretical evidences, such as the hierarchy problem, baryogenesis and the number of families and a few experimental data (neutrino masses, dark matter and dark energy) suggest that we should look for physics beyond the Standard Model (SM). Some of these problems are solved in an important class of models, which assume the existence of additional spatial symmetries, called supersymmetry. The objective of this thesis is to study the concept of supersymmetry and its potential relevance to the physics beyond the Standard Model. To understand the principle of supersymmetry we will construct the Minimal Supersymmetric Standard Model (MSSM) and present some of its phenomenological consequences. We will also present the mSUGRA and mGMSB models, as well as some of its properties. In the Appendix we show some complementary information and a parallel work developed during this project
Mestrado
Física das Particulas Elementares e Campos
Mestre em Física
4
Ali, T. "String theory and conformal field theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595446.
Анотація:
In this thesis we consider some aspects of two dimensional Conformal Field Theory and their connection to String Theory. We have also studied some aspects of supersymmetry of M-Theory on Ricci-flat seven manifolds with 4-form fluxes. We concentrate mainly on certain supersymmetric extensions of the coset models due to Goddard, Kent and Olive (GKO). These models are known as the Kazama-Suzuki (KS) models and they are characterized by their N = 2 superconformal symmetry. Two series of the KS models enjoy a duality called level-rank duality which can be described roughly as duality between the dimension of the target space and the level of coset. We believe that the path-integral approach is the closest in spirit to string theory. Therefore, we formulate the level-rank duality of KS models in the path-integral approach by using the realization of GKO cosets as gauged Wess-Zumino-Novikov-Witten (gauged-WZNW) models. We derive, for a class of KS models, an expression for the partition function which is symmetric in the parameters of the level-rank duality. We compute the central charge of the models from this expression which matches that of Kazama and Suzuki in the operator approach. We then work out the target space metric and the dilation of the gauged-WZNW model based on the GKO coset SU(3)/(SU(2) x U(1)). It turns out to be quite a complicated metric with a non-trivial dilation. We verify, as a consistency check, that they satisfy the appropriate string theory effective equations of motion. We then argue that this background can arise naturally in type II string theory compactified down to AdS3 space. We then turn to Eleven Dimensional Supergravity which is the low energy limit of M-theory. We adopt a metric ansatz which is a warped product of four dimensional Minkowski space and a (non-compact) seven manifold with 4-form fluxes turned on it. We derive the condition for unbroken supersymmetry with fluxes and non-trivial warp-factor. We show that the same condition implies that the seven manifold is conformal to a Ricci-flat manifold. We also point out the limitation of some naive ansatze about the structure of the Killing spinor. At this stage we are unable to give an explicit solution to the supersymmetry condition.
5
Muenster, Korbinian. "String field theory." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-160964.
Анотація:
This thesis discusses several aspects of string field theory. The first issue is bosonic open-closed string field theory and its associated algebraic structure -- the quantum open-closed homotopy algebra. We describe the quantum open-closed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum open-closed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a non-trivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background.
Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms.
Finally, we outline the construction of type II superstring field theory. Specific features of the superstring are the appearance of Ramond punctures and the picture changing operators. The sewing in the Ramond sector requires an additional constraint on the state space of the world sheet conformal field theory, such that the associated symplectic structure is non-degenerate, at least on-shell. Moreover, we formulate an appropriate minimal area metric problem for type II world sheets, which can be utilized to sketch the construction of a consistent set of geometric vertices. The algebraic structure of type II superstring field theory is that of a $\mathcal{N}=1$ loop homotopy Lie algebra at the quantum level, and that of a $\mathcal{N}=1$ homotopy Lie algebra at the classical level.
6
Bouda, Ahmed. "Localisation de la symétrie BRST en théorie des cordes." Bordeaux 1, 1989. http://www.theses.fr/1989BOR10531.
Анотація:
La symetrie brst locale pour une classe generale d'actions fixees de jauge de la corde bosonique est utilsiee pour etudier les anomalies possibles de l'algebre des courants brst correspondants. Une analyse analogue est faite pour la theorie conforme obtenue en introduisant les differentielles de beltrami. Une nouvelle algebre brst locale pour le groupe de weyl x lorentz x lorentz x diffeomorphisme est construite dans un espace a n-dimensions. Elle est appliquee pour n=2 a la corde bosonique et pour n=4 a la gravite d'einstein
7
Murata, Masaki. "No-Ghost Theorem and Gauge Fixing Problem in Open Superstring Field Theory." 京都大学 (Kyoto University), 2011. http://hdl.handle.net/2433/142377.
8
Gaberdiel, Matthias Reinhard. "Chiral conformal field theory." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387671.
9
Fring, A. "Affine Toda field theory." Thesis, Imperial College London, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295149.
10
Lewis, Alexander. "Logarithmic conformal field theory." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268249.
11
Nichols, Alexander. "Logarithmic conformal field theory." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249439.
12
Saffin, Paul Matthew. "Field theory in cosmology." Thesis, University of Sussex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266442.
13
Abramov, Gueorgui. "Nilpotent Class Field Theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14361.
14
Ricotta, Regina Maria. "Topics in field theory." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46281.
15
Russell, Katherine. "Field theory and solitons." Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2205.
16
Halter, Sebastian. "Inflation from field theory and string theory perspectives." Diss., Ludwig-Maximilians-Universität München, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-156269.
17
Bedford, James Andrew Peter. "On perturbative field theory and twistor string theory." Thesis, Queen Mary, University of London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.479158.
18
Mohamed, Adam. "Local Class Field Theory via Lubin-Tate Theory /." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1936.
19
Karch, Andreas. "Field Theory Dynamics from branes in String Theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 1998. http://dx.doi.org/10.18452/14371.
Анотація:
Nach jahrelanger Suche hat sich bis heute Stringtheorie als einziger Kandidat einer konsistenten Quantentheorie der Gravitation herauskristallisiert. Um aus der Stringtheorie präzise Vorhersagen für unsere Niederenergiewelt zu gewinnen, ist es notwendig, das Vakuumproblem zu lösen, das heißt einen Mechanismus zu finden, der aufzeigt, in welchem Stringvakuum wir leben und warum die Natur dieses ausgewählt hat. Die Beantwortung dieser Frage benötigt nicht-perturbative Informationen.Diese wurden erst in jüngster Zeit zugänglich. Eine besondere Rolle in dieser Entwicklung spielten die sogenannten D-branes. Sie stellen mögliche nicht-perturbative Beiträge zu Stringamplituden dar. Die Identifizierung, daß D-branes einfach Objekte sind, auf denen Strings enden können, ermöglicht sie zu handhaben und zu zeigen, daß ihre Dynamik im wesentlichen durch Eichtheorien erfaßt wird. D-branes erlaubten, zahlreiche Dualit\ätssymmetrien zu etablieren, deren Haupta ussage zu sein scheint, daß alle 5 Stringtheorien sowie 11d Supergravitation nur verschiedene perturbative Limites einer fundamentalen 11d Theorie sind, T-Theorie. In dieser Arbeit habe ich mich mit einigen Anwendungen dieser Ideen beschäftigt. Die Tatsache, daß D-branes durch Super Yang-Mills Theorien beschrieben werden, erlaubt uns einen Stringhintergrund derart zu präparieren, daß wir nahezu jede Eichtheorie als relevante Niederenergiebeschreibung erhalten können. Eine besonders verbreitete Variante dieser Idee sind die sogenannten ``Hanany Witten setups'', in denen dieser Stringhintergrund nur aus flachen branes im flachen Raum besteht. Mit Hilfe dieser Technik habe ich verschiedene Dualitätssymmetrien in Feldtheorien auf Stringdualitäten zurückgeführt. Ferner ist es möglich, mit Hilfe der branes die Existenz nicht trivialer Fixpunkt Theorien in sechs Dimensionen zu beweisen und einige ihrer Eigenschaften zu analysieren. Einige dieser Fixpunkte beschreiben Phasenübergänge zwischen verschiedenen brane Hintergründen. Unter anderem läßt es sich auf diese Weise zeigen, daß es in 4 Dimensionen Übergänge zwischen chiralen und nicht chiralen Vacua gibt. Ferner wurde gezeigt, daß alle anderen Zugänge zu dem Problem, Eichtheorien in Stringtheorie einzubetten, im wesentlichen äquivalent zum HW Ansatz sind, in dem Sinn, daß die entsprechenden Stringhintergründe dual zueinander sind. Dadurch können neue Aspekte der String T-Dualität verstanden werden, so wie z.B. T-Dualitäat für brane Segmente und gebogene branes.Außerdem erlaubt uns diese Verbindung, die Phasenübergänge, die wir im HW Bild entdeckt haben, tatsächlich als Übergänge zwischen topologisch verschiedenen Stringkompaktifizierungen zu verst ehen.In this thesis I discussed several applications of the connection of non-perturbative string theory and SYM theory. In Chapter 1 I reviewed the physics of D-branes as one example of a non-perturbative effect in string theory. Their dynamics is dominated by gauge theory. This fact can be used to engineer certain string backgrounds which yield interacting SYM theories as their low-energy description. In Chapter 2 I then introduced one of the approaches in detail, the HW setup. I gave a summary of the identification of the classical gauge theory, showed how quantum effects manifest themselves in the brane picture and how to solve them. This way of embedding gauge theories into string theories has several interesting applications. These were the topic of Chapter 3. First I discussed dualities in field theory and showed how they arise as a natural consequence of string duality. As a second application I used branes to prove the existence of non-trivial fixed point theories in 6 dimensions and to study their properties. Some of these fixed points describe phase transitions between two different brane configurations. From a 4d point of view these 6d transitions can induce a chiral non-chiral transition. In Chapter 4 I discussed the relation of the HW setup with the other approaches of embedding gauge theory into string theory, especially the branes as probes approach. The different ways of embedding gauge theories in string theory are shown to be actually T-dual as string backgrounds. For one this allowed us to explore several new aspects of T-duality, like T-duality for bended branes and branes endin g on branes. In addition this relation can be used to show that the transitions found in the brane picture can as well be understood as transitions between topologically distinct compactifications of string theory. Some open problems and directions for further research were mentioned in Chapter 5.
20
Lake, Matthew James. "Cosmic necklaces in string theory and field theory." Thesis, Queen Mary, University of London, 2010. http://qmro.qmul.ac.uk/xmlui/handle/123456789/523.
Анотація:
In this thesis we investigate astrophysical phenomena which arise in models with compact extra dimensions, focussing on the cosmological consequences of strings which wrap cycles in the internal space. Embedding our strings in the Klebanov-Strassler geometry we develop a concrete model of cosmic necklaces and investigate the formation of primordial black holes and dark matter relics from necklace collapse. Using data from the EGRET cosmic ray experiment, we place bounds on the parameters which de ne the warped deformed conifold, including the value of the warp factor and the radius of the compact space. Chapter 1 provides a brief overview, while background material is included in chapter 2, and these results are presented in chapter 3. In chapter 4 we analyse the dynamics of wound strings with angular momentum in the compact dimensions and determine the equation of motion for a self-oscillating loop. Finally, in chapter 5 we suggest a eld-theoretic dual for wound-string necklaces based on a modi cation of the standard Abelian-Higgs model. After introducing spatially-dependent couplings for the scalar and vector elds, we propose a static, non-cylindrically symmetric solution of the resulting eld equations which describes a \pinched" string with neighbouring vortex and anti-vortex regions. The similarities between pinched strings and the four-dimensional appearance of wound-string states are then examined and a correspondence between eld theory and string theory parameters is suggested. We nd that the topological winding number of the eld theory vortex may be expressed in terms of parameters which de ne the winding of the dual string around the compact space. According to this relation, the topological charge is equal to unity when the string has zero windings, and the standard Nielsen-Olesen duality is recovered in this limit. One key result of this work is an estimate of the Higgs boson mass (at critical coupling) in terms of the parameters which de ne the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.
21
Feng, Bo 1971. "D-branes, gauge theory and string field theory." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8491.
Анотація:
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.Includes bibliographical references (p. 245-262).
In this thesis, we present several works done in last three years. They include three directions in the string theory. In the first direction, we use the brane setup to find mirror pairs of SO(n) and Sp(k) gauge groups for N = 4 three-dimensional gauge field theories. To reach this result, we analyze carefully the s-configuration and predict a nontrivial string dynamics, i.e., the splitting of branes on the orientifold planes. In the second direction, we develop the "inverse algorithm" and use it to get nontrivial world volume theories of D-branes probing more exotic singularities. In this process, we find the "toric duality" which relates different phases of D-brane probe theories. We realize later that the toric duality is an example of the more powerful Seiberg-duality so these different phases are related by the Seiberg duality. In the third direction, by using numerical calculation we get a strong evidence to support the second conjecture of Sen's three conjectures. We show that if the identity field is BRST exact state around the tachyon vacuum, the open string spectrum will decouple from the physics and leave only the closed string spectrum.
by Bo Feng.
Ph.D.
22
Soares, Caio Gilbert Juan E. "A class-specific ensemble feature selection approach for classification problems." Auburn, Ala, 2009. http://hdl.handle.net/10415/1659.
23
Kawai, S. "Boundary conformal field theory in free-field representation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249280.
24
Schäfer-Nameki, Sakura. "D-branes in boundary field theory and K-theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620017.
25
Huyal, Ulas. "Conformal Symmetry In Field Theory." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613136/index.pdf.
Анотація:
In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.
26
Endres, Michael G. "Topics in lattice field theory /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/9713.
27
Wang, Yuhao. "Advanced Theory of Field Curvature." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/325494.
Анотація:
Classical field curvature theory emphasizes the Petzval theorem, which models field curvature aberration to the 4th order. However, modern lens designs use aspheric surfaces. These surfaces strongly induce higher order field curvature aberration which is not accounted for Petzval field curvature. This dissertation focuses on developing higher order field curvature theories that are applied to highly aspheric designs. Three new theories to control field curvature aberration are discussed. Theory 1: an aspheric surface that is close to the image and has two aspheric terms sharply reduces field curvature by 85%. Theory 2: an aspheric surface that is farther from the image plane induces astigmatism to balance Petzval field curvature. Theory 3: oblique spherical aberration can be induced to balance Petzval field curvature. All three theories are applied to real design examples including the following lenses: cellular phone, wide angle, fast photographic, and zoom lenses. All of the analyses results are consistent with the theories. Moreover, two types of novel aspheric surfaces are proposed to control field curvature. Neither of the surfaces are polynomial-type surfaces. Examples show that the novel aspheric surfaces are equivalent to even aspheric surfaces with two aspheric coefficients in terms of field curvature correction. The study on field curvature correction using aspheric surfaces provides an alternative method to use when aspheres are accessible. Overall, this dissertation advances the theory of field curvature aberration, and it is particularly valuable to evaluate highly aspheric designs when Petzval theory is inapplicable.
28
Gill, Alasdair James. "Field theory and topological defects." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244675.
29
Gandra, Pedro Manuel Fernandes de ArauÌjo. "Stochastic equations in field theory." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430874.
30
Ivin, Marko. "Topics in quantum field theory." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410042.
31
Hatlo, Marius Mortensen. "Field theory of electrolyte solutions." Thesis, University of Manchester, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.494601.
Анотація:
The main goal of the project has been to develop a better microscopic description of electrostatic interactions in colloidal systems. We have developed a variational field theory that consistently incorporates ion-ion correlation effects, dispersion interactions, and image charge interactions. This theory has been applied to investigate the influence of electrolytes on the interaction between colloidal particles at low to moderate electrolyte concentrations. The theory has also been modified to study coulomb systems in the strong coupling regime. This theory has been applied to study the interaction between charged surfaces with neutralizing counterions and salt, with good agreement between theory and simulation. We have also studied specific-ion effects, such as the Hofmeister series, which has been a long standing problem in chemistry and biology. In particular, we have included ion polarizability in the theory and studied the double layer interaction at the mean field level.
32
Russell, I. H. "Calculations in quantum field theory." Thesis, University of Newcastle Upon Tyne, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328134.
33
Douglas, Michael R. Schwarz John H. "G/H conformal field theory /." Diss., Pasadena, Calif. : California Institute of Technology, 1988. http://resolver.caltech.edu/CaltechETD:etd-08202008-083708.
34
Kwak, Seung Ki. "Topics in double field theory." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/79518.
Анотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 199-204).
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and M = 1 super-gravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O(D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group 0(D, D) and the theory displays Spin+(D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the K = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local 0(1, 9 + n) x 0(1, 9) tangent space symmetry under which the fermions transform.
by Seung Ki Kwak.
Ph.D.
35
Janse, van Rensburg Esaias Johannes. "Field theory and random walks." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328723.
36
Dove, Justin(Justin Michael). "Theory of phasor-field imaging." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/127015.
Анотація:
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 141-143).
Phasor-field (P-field) imaging is a promising recent solution to the task of non-line-of-sight (NLoS) imaging, colloquially referred to as "seeing around corners". It consists of treating the oscillating envelope of amplitude-modulated, spatially-incoherent light as if it were itself an optical wave, akin to the oscillations of the underlying electro- magnetic field. We present a formal analysis of P-field propagation using paraxial wave optics and demonstrate how it can be used to form images of hidden diffuse targets both computationally and with physical lenses. In both cases, we find that hidden target planes can be imaged at the modulation-wavelength diffraction limit, despite the presence of intervening diffusers. To model propagation through more general scenarios, we introduce the two-frequency spatial Wigner distribution and derive primitives that characterize its behavior. These primitives are used to analyze occlusion-aided imaging scenarios as well as to verify intuitive results in the geometric-optics limit. Consistent with prior work, we find that intervening occluders offer the potential to form convolutional images of hidden target planes, even in the absence of time-of-flight information. Additionally, we demonstrate how to extend our frame-work beyond the paraxial regime and include a thorough exploration of the effects of speckle, which we find are likely manageable in realistic scenarios.
by Justin Dove.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science
37
Farmer, Matthew Ray. "Applications in Fixed Point Theory." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4971/.
Анотація:
Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
38
Chibane, Khaled. "Applications of field-evaporation theory." Thesis, Aston University, 1985. http://publications.aston.ac.uk/10584/.
39
Lewis, Peter M. "Community media : field, theory, policy." Thesis, London Metropolitan University, 2010. http://repository.londonmet.ac.uk/1217/.
Анотація:
The submission consists of twenty-three outputs, spanning over three decades. These range from books and chapters to reports, journal articles and edited publications. The accompanying commentary aims to set the submitted work in context, demonstrate that it constitutes a coherent whole, and that it makes an independent and original contribution to knowledge and the advancement of the academic field of community media within the discipline of media studies. A number of overlapping contexts are summarised: the socio-historical setting in which the practice of electronic community media first emerged; the ‘personal/professional’ context in which reflection on practical experience led to developments in theory and policy analysis; the academic context of the development of British media studies where at first radio was marginalised and there was no discursive space for the notion of community media, then a later stage where a wider range of theoretical contexts brought community and alternative media into the academic frame. Three main sections discuss, respectively, the candidate’s contribution to the identification and categorisation of community media, the application to it of theoretical perspectives, and the development of policy analysis. All three areas, it is argued, were part of a wider strategy aimed at bringing recognition to the field and which involved activities outside the scope of the submission (advocacy, interventions in mainstream media) but which are part of the context of the submitted work. For that reason an appendix (B) lists all the candidate’s publications on the subject, while others list conference presentations and other relevant activities. In addition, the documentation includes a brief career summary and statements by co-authors.
40
Baguet, Arnaud. "Exceptional Field Theory and Supergravity." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN022/document.
Анотація:
Dans cette thèse, nous présentons des avancements récents en Théorie des Champs Doubles (TCD) et Théories des Champs Exceptionnels (TCE). Ces théories ont la particularité d’être des reformulations de supergravité dans lesquelles les symétries de dualité sont explicites avant toute réduction dimensionnelle. Ces reformulations se basent sur la définition d’un espace-temps étendu qui géométrise le groupe de T-dualité en TCD et les groupes exceptionnels de U-dualité en TCE. Tous les champs de cet espace sont soumis à une contrainte de section qui restreint leur dépendance en coordonnées. Il existe plusieurs solutions à la contrainte de section, qui correspondent donc à des théories différentes. Dans ce sens, le formalisme des théories des champs étendues amène à une unification de ces théories. De plus, grâce à un outil spécifique aux théories des champs étendues, l’ansatz de Scherk-Schwarz généralisé, il est possible de réécrire les ansatz compliqué de type Kaluza-Klein en supergravité sous une forme élégante et compacte: un produit matriciel en dimensions supérieures. Ici, nous présentons plusieurs exemples de l’efficacité de l’ansatz de Scherk-Schwarz généralisé. En particulier, nous prouvons deux conjectures concernant les troncations cohérentes: la réduction dite “de Pauli” de la corde bosonique ainsi que la supergravité de type IIB sur AdS5 x S5. La dernière application de cet ansatz concerne la théorie de type IIB généralisée, apparue récemment dans l’étude des système intégrables, et son plongement dans la TCE E6(6). Enfin, nous présentons la complétion supersymétrique de la TCE E8(8) bosoniqueIn this thesis, recent developments in Double Field Theory (DFT) and Exceptional Field Theory (EFT) are presented. They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. This is achieved through the definition of an extended spacetime that “geometrises” the T-duality group O(d,d) in DFT and exceptional U-duality groups in EFT. All functions on this extended space are subject to a covariant `section constraint', whose solutions then restrict the coordinates dependency of the fields. There exist different solutions to the section constraint that correspond to different theories. In this sense, different theories are unified within the formalism of extended field theories. Moreover, extended field theories possess a powerful tool to study compactifications: the generalised Scherk-Schwarz ansatz.Here, we present several examples of the effectiveness of the generalised Scherk-Schwarz ansatz. In particular, we proved two conjectures regarding consistent truncations: the so-called Pauli reduction of the bosonic string on group manifolds and type IIB supergravity on AdS5 x S5. Another application is presented on the embedding of generalised type IIB within the E6(6) EFT, which recently appeared in the study of integrable systems.Finally, we present the supersymmetric completion of the bosonic E8(8) EFT
41
Johannes, Michael T. "A fixed-point phase lock loop in a software defined radio." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2002. http://library.nps.navy.mil/uhtbin/hyperion-image/02sep%5FJohannes.pdf.
42
Castilho, C. M. C. de. "Theory of field ionization in the field ion microscope." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373668.
43
Troost, Jan. "Strings, links between conformal field theory, gauge theory and gravity." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00410720.
Анотація:
La théorie de cordes unifie de façon naturelle les théories de jauge, qui décrivent les interactions entre les particules élémentaires, avec une théorie quantique de la gravitation. Ces dernières années ont apporté de grands progrès dans la compréhension des états non-perturbatifs de la théorie, ses aspects holographiques, ainsi que la construction de modèles proches du Modèle Standard. Néanmoins, il reste des défis pour la théorie de cordes, qui incluent une définition non-perturbative, une meilleure compréhension de l'holographie, et le problème de la constante cosmologique. Ma recherche s'est concentrée sur des aspects formels des théories de gravitation quantique, qui incluent les trous noirs, la dépendance du temps, et l'holographie. Gr^ace à de nouveaux résultats dans le domaine de la théorie conforme avec spectre continu, mes collaborateurs et moi-m^eme avons avancé dans la compréhension de l'holographie dans des fonds avec dilaton linéaire, ainsi que dans le plongement de théories de jauge supersymétriques dans la théorie de cordes. En particulier, on a étudié des théories conformes supersymétriques avec spectre continu que l'on utilise pour construire des fonds de théories de cordes non-compacts et courbés. Les résultats obtenus nous ont permis de décrire des exemples explicites de symétrie miroir pour des fonds non-compacts. En introduisant des bords dans les théories conformes, on a analysé des états non-perturbatifs de la théorie de cordes, les D-branes. A basse énergie, les degrés de liberté sur les D-branes interagissent par des interactions de jauge. Avec ces outils, on a réussi à plonger une dualité infrarouge de théorie de jauge supersymétrique dans la théorie de cordes, et on a montré que la dualité correspond à une monodromie pour les états de bord dans l'espace de modules de la théorie conforme.Dans cette thèse, on discute de nombreux autres liens entre la théorie conforme, la théorie de jauge et la gravitation. La plupart des contributions décrites étaient motivées par la théorie de cordes. Des exemples sont l'analyse d'états qui préservent la supersymétrie et leur lien avec les algèbres affines, la dépendance du temps et le dictionnaire holographique, l'analyse directe de la quantification de la gravité en présence d'un trou noir, la réalisation du scenario sans-bord pour la fonction d'onde de l'univers en théorie de cordes, une formule de Verlinde pour les théories conformes non-rationnelles et la construction de solutions non-géometriques à la supergravité. Dans d'autres travaux, je me suis concentré sur des théories qui quantifient la gravité plus directement, mais qui pourraient avoir moins de succès dans le problème de l'unification des forces en quatre dimensions. Ces théories ont quand-m^eme le potentiel de nous apprendre des aspects communs à toute théorie de gravitation quantique. Par exemple, on a analysé les degrés de liberté responsables de l'entropie d'un trou noir en trois dimensions, et nous avons argumenté sur la difficulté de reconcilier l'invariance modulaire avec l'unitarité en dehors de la théorie de cordes. On a aussi discuté la diffusion de ces trous noirs. D'autres contributions à la théorie de jauge non-commutative, la théorie de jauge supersymétrique, la production de paires dans un espace courbe, et cetera, sont aussi relativement indépendantes du cadre de la théorie de cordes.
Il me semble qu'il reste intéressant d'étudier des questions difficiles sur la théorie de jauge et la gravitation quantique, dans la cadre de la théorie de cordes, et en dehors de ce cadre, et d'^etre guidé par des problèmes ouverts durs qui doivent mener à un progrès concret par incréments ou par sauts.
44
Mazur, Daniel Paul. "Nonperturbative quantum field theory in astrophysics." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/43255.
Анотація:
The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.
In the early universe, quantum fluctuations of a scalar field result in the generation of particles, and of the density fluctuations which seed the large- scale structure of the universe. These fluctuations are generated through quantum processes, but are ultimately treated classically. We explore how a quantum-to-classical transition may occur due to non-linear self-interactions of the scalar field. This mechanism is found to be too inefficient to explain classicality, meaning fields which do not become classical because of other mechanisms may maintain some evidence of their quantum origins.
Magnetars are characterized by intense magnetic fields. In these fields, the quantum vacuum becomes a non-linear optical medium because of interactions between light and quantum fluctuations of electron-positron pairs. In addition, there is a plasma surrounding the magnetar which is a dissipative medium. We construct a numerical simulation of electromagnetic waves in this environment which is non-perturbative in the wave amplitudes and background field. This simulation reveals a new class of waves with highly non-linear structure that are stable against shock formation.
The dense nuclear material in a neutron star is expected to be in a type-II superconducting state. In that case, the star’s intense magnetic fields will penetrate the core and crust through a dense lattice of flux tubes. However,
depending on the details of the free energy associated with these flux tubes, the nuclear material may be in a type-I state which completely expels the field. We compute the quantum corrections to the classical energies of these flux tubes by creating a new, massively parallel Monte-Carlo simulation. The quantum contribution tends to make a small contribution which adds to the classical free energy. We also find a non-local interaction energy with a sign that depends on the field profile and spacing between flux tubes.
45
Jakovljevic, Cvjetan, and University of Lethbridge Faculty of Arts and Science. "Conformal field theory and lie algebras." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 1996, 1996. http://hdl.handle.net/10133/37.
Анотація:
Conformal field theories (CFTs) are intimately connected with Lie groups and their Lie algebras. Conformal symmetry is infinite-dimensional and therefore an infinite-dimensional algebra is required to describe it. This is the Virasoro algebra, which must be realized in any CFT. However, there are CFTs whose symmetries are even larger then Virasoro symmentry. We are particularly interested in a class of CFTs called Wess-Zumino-Witten (WZW) models. They have affine Lie algebras as their symmentry algebras. Each WZW model is based on a simple Lie group, whose simple Lie algebra is a subalgebra of its affine symmetry algebra. This allows us to discuss the dominant weight multiplicities of simple Lie algebras in light of WZW theory. They are expressed in terms of the modular matrices of WZW models, and related objects. Symmentries of the modular matrices give rise to new relations among multiplicities. At least for some Lie algebras, these new relations are strong enough to completely fix all multiplicities.iv, 80 leaves : ill. ; 28 cm.
46
Rondelli, Andrea. "Functional methods in quantum field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15839/.
Анотація:
Iniziamo introducendo l'integrazione su manifold di Hilbert, tramite l'approssimazione dello spazio tangente alla varietà. Passiamo poi a descrivere due tecniche per regolarizzare integrali funzionali o di cammino quadratici (che presentano un laplaciano nell'azione): la regolarizzazione e rinormalizzazione tramite zeta function e il cutoff nel tempo proprio. Cerchiamo di confrontare i due diversi risultati (finiti) così ottenuti. Sussessivamente applichiamo l'integrazione funzionale agli integrali di cammino usando il formalismo della quantizzazione in qp-simboli ottenendo così un'ampiezza di probabilità. Infine iniziamo a sviluppare questi argomenti per le teorie di gauge. In particolare ci soffermeremo su vari aspetti geometrici dei campi di gauge, quali la connessione e la curvatura (usando il formalismo dei fibrati). In ultimo introduciamo l'integrazione funzionale per le teorie di gauge.
47
Hofmann, Walter. "Class field theory for arithmetic schemes." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985500964.
48
Díaz, Calzadilla Pablo. "Scalar stars and effective field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23167/.
Анотація:
The axion is one of the favored candidates to form the cold dark matter in the universe. This pseudo-scalar field may form compact objects called axion stars, whose physics is well captured by means of non-relativistic effective field theory coupled to Newtonian gravity. The interplay between gradient energy, self-interactions and gravity gives rise to both dilute and dense axion stars. While the existence of the dilute axion stars is well established, the situation is more complicated in the case of the so-called dense axion stars, an extra physically stable solution of the system of differential equations describing the dynamics of the axion field in the regime where self-interactions play an important role. The existence of the dense axion stars has not been settled in the literature.
In this thesis, we discuss first the appropriate non-relativistic formalism for the study of these clumps by means of the various non-relativistic reductions found in the literature. We analyze the stability, for different sizes and number of particles, of these objects considering quartic self-interaction potentials. This allows us to corroborate the results for these cases already presented by other authors. We also go beyond the simplest case, by analyzing more complicated potentials describing with higher precision the axion self-interactions. By employing the correct non-relativistic axion effective field theory we show that the dense branch is an artefact of the non-relativistic reduction procedure.
49
Uhlmann, Sebastian. "String field theory methods and solutions /." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969730179.
50
Pinnow, Henryk A. "Field theory of interacting crumpled manifolds." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=96624687X.