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1
Huyal, Ulas. "Conformal Symmetry In Field Theory." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613136/index.pdf.
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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.
2
Sonnenschein, Jonas [Verfasser]. "Mean-field theory and projective symmetry group classifications of quantum spin liquids / Jonas Sonnenschein." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1220288179/34.
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Juršėnas, Rytis. "Algebraic development of many-body perturbation theory in theoretical atomic spectroscopy." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20101223_153004-84982.
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The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences.Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose.
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Germano, Guilherme Rocha. "Representações irredutíveis unitárias do grupo de Poincaré." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-08122016-160042/.
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A teoria de representações de grupos topológicos Hausdorff, localmente compactos e separáveis em espaços de Hilbert separáveis é introduzida, especificada para grupos compactos e comutativos e são obtidas realizações explicitas das representações finitas irredutíveis de $SU(2)$, $SO(3)$, SL(2,C) e $SO(1,3)^{\\uparrow}$. A teoria das representações induzidas é então apresentada e, depois de feita a conexão entre teorias quântico relativísticas livres no espaço plano de Minkowski e representações unitárias irredutíveis de $R^4 times$ SL(2,C), aplicada para obter tais representações e realizar explicitamente os casos correspondentes a partículas elementares com spin definido em espaços que não admitem a definição de operadores de reflexão espacial. A inclusão da operação de reflexão espacial é feita através de uma variação do método das representações induzidas que conduz a representações unitárias {\\bf redutíveis} de $R^4 times$ SL(2,C) para as quais são obtidas equações de onda selecionando espaços irredutíveis, os quais definem partículas elementares admitindo paridade no contexto das teorias quânticas de campos livres.The theory of locally compact, second countable and Hausdorff topological group representations in separable Hilbert spaces is introduced, and specified to compact and commutative groups. Explicit realizations of the finite irreducible representations of $SU(2)$, $SO(3)$, SL(2,C) and $SO(1,3)^{\\uparrow}$ are obtained. The theory of induced representations is then presented and, after the connection between quantum relativistic free theories in flat Minkowski space and unitary irreducible representations of $R^4 times$ SL(2,C) is made, it is applied and used to classify these representations. Explicit realizations of the cases corresponding to elementary particles with definite spin in spaces which do not allow spacial reflection operators are presented. Spacial reflections are carried with a variation of the induced representation method that leads to unitary {\\bf reducible} representations of $R^4 times$ SL(2,C). Wave equations selecting irreducible spaces that define elementary particles admitting parity in quantum free field theories are derived.
5
Bone, Richard George Andrew. "New applications of the molecular symmetry group." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239761.
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Johnson, Samuel Buck. "Enhanced gauge symmetry in 6D F-theory." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104507.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 142-153).
This thesis reports on progress in understanding the set of 6D F-theory vacua. F-theory provides a strikingly clean correspondence between physics and physical quantities and mathematics and geometrical quantities, which allows us to make precise mathematical statements using well defined and understood methods. We present two related results that both serve the following principal goal: to understand the set of 6D F-theory vacua using geometrical methods, and then to compare these to low-energy supergravities. In doing so, we find a near-perfect correspondence between low-energy supergravities that can be obtained from F-theory and field theories that satisfy known low-energy consistency conditions, e.g. anomaly cancellation. However, we will also isolate several cases that we prove can never arise in F-theory yet have no visible lowenergy inconsistencies. The results are presented in two chapters. First, we describe a complete, systematic enumeration of all elliptically fibered Calabi-Yau threefolds (EF CY3s) with Hodge number h²,¹ >/= 350; physically, this classifies all F-theory models that lead to low-energy supergravities with >/= 351 neutral hypermultiplets. This result is obtained using global geometric calculations in finitely many, specific geometries. Second, we classify which local geometrical structures, corresponding to combinations of gauge algebras and (potentially shared) matter, can arise in F-theory. This classification is performed using local geometric calculations. This investigation reveals an exceedingly tight correspondence between F-theory models and consistent low-energy supergravities. Indeed, this near-perfect agreement provides a backdrop against which discrepancies between F-theory and low-energy supergravities stand out in sharp contrast. We describe in detail these discrepancies, in which seemingly consistent field theories cannot be described in F-theory. This work has several implications. First, it further refines the understanding of 6D supergravity models in F-theory, which has implications for string universality in 6D. It adds a level of mathematical precision to the study of 6D superconformal field theories (SCFTs) begun in [4, 3], which is a conjecturally complete classification of all 6D SCFTs. Our analysis confirms many of their results, but also explicitly shows that some of their proposed models cannot in fact be realized through their construction. Since our results can be phrased in terms of geometry, they also have implications for the study of EF CY3s. Finally, we discuss the subset of our results that hold in 4D F-theory as well, where they provide additional structure in a still difficult-to-constrain landscape.
by Samuel Buck Johnson.
Ph. D.
7
Carteret, Hilary Ann. "Symmetry and multiparticle entanglement." Thesis, University of York, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341118.
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Bergman, Oren. "Nonrelativistic conformal symmetry in 2+1 dimesional field theory." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/32619.
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Mantry, Gautam. "Heavy quark symmetry in the soft collinear effective theory." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32309.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (leaves 189-198).
We study strong interaction effects in nonleptonic decays of ... mesons with energetic particles in the final state. An introduction to Soft Collinear Effective Theory (SCET), the appropriate effective field theory of QCD for such decays, is given. We focus on decays of the type ... where M is a light energetic meson of energy E. The SCET formulates the problem as an expansion in powers of where Q [approx.] ... . A factorization theorem is proven at leading order that separates the physics of the scales ... . In addition, the factorization theorem decouples energetic degrees of freedom associated with the light meson allowing us to derive heavy quark symmetry relations between the ... type amplitudes. A new mechanism for the generation of non-perturbative strong phases is shown within the framework of factorization. Heavy quark symmetry relations are shown to apply for these strong phases as well. Furthermore, the strong phases for certain light mesons in the final state are shown to be universal. The analysis is extended to ... type decays with isosinglet light mesons and excited charmed mesons in the final state respectively. A host of other phenomenological relations are derived and found to be in good agreement with available data.
by Gautam Mantry.
Ph.D.
10
Lin, Zhou. "Theoretical Studies on the Spectroscopy and Dynamics of Astrochemically Significant Species." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429633299.
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Wiedemann, Urs Achim. "Constraints and spontaneous symmetry breaking in quantum field theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336764.
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Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-61).
Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth by Dmitry A. Vaintrob.
Ph. D.
13
Abdelhady, A. M. H. H. "Scattering in soliton models and crossing symmetry." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71664.
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Thesis (MSc)--Stellenbosch University, 2012.ENGLISH ABSTRACT: Crossing symmetry relates scattering and annihilation processes to each other. Its derivation is straightforward in perturbative approaches to quantum field theory: it merely reflects the exchange of in- and outgoing states in Feynman diagram computations. In soliton models, the situation is much more complicated because the scattering and the annihilation processes concern distinct topological sectors that are not related by any continuous transformation. In this thesis a simple soliton model will be employed to address this problem numerically. First, in the unit topological sector we extract asymptotically the phase shift of the scattering process of a wave packet off the kink-solution. To this end we solve the time-dependent equation of motion of the non-integrable '4 field model in (1+1) spacetime dimensions for two distinct initial conditions: the wave packet in a trivial vacuum background and in the background of the kink-solution. Second, in the topologically trivial sector we present numerical solutions of the kink– antikink interaction in the same model. We find that the final state of this interaction varies dramatically with the impact velocity. As result, we analyze our numerical solutions for the kink–antikink collisions system in two regimes. For the initial velocity of the system less than some critical velocity, vc 0:26, the kink and the antikink either annihilate or inelastically scatter. On the other hand, the kink and the antikink always inelastically scatter when the initial velocity of the system is higher than this critical velocity. However, the scattering processes of the kink–antikink with initial velocity below and above the critical velocity are different. Below the critical velocity the kink and the antikink collide and always undergo n-bounces (n 2) before they depart to infinity. When the initial velocity of the system is higher than vc, the kink and the antikink depart to infinity after only one bounce. We present a qualitative description for these bounce effects between the kink and the antikink motivated by earlier studies as well as our numerical simulations. We utilize collective coordinates to study the dynamics of the kink–antikink system in two degrees of freedom. In this regime, we modify the ansätze of the kink–antikink system from earlier studies to account for relativistic effects. We perform a comparison between this approximation and the full system. We end our discussion of this sector by discussing the scattering data for the inelastic scattering and the annihilation processes of the kink–antikink. Third, we compare the extracted scattering data for the scattering process of a wave packet off the kink-solution and the annihilation process of the kink–antikink to each other. Finally, these studies of different sectors allow us to make a conjecture about the validity of crossing symmetry within the non-integrable '4 field model.
AFRIKAANSE OPSOMMING: Kruising-simmetrie beskryf ’n verband tussen verstrooiings- en vernietigingsprosesse. Die afleiding daarvan binne die raamwerk van steuringsteorie is eenvoudig: dit behels bloot die omruil van ingaande en uitgaande toestande in die Feynman-diagram. In soliton-modelle is die situasie egter meer ingewikkeld aangesien die verstrooiings- en vernietigingsprosesse in verskillende topologiese sektore plaasvind wat nie deur kontinue transformasies aan mekaar gekoppel is nie. In hierdie tesis word daar van ’n eenvoudige soliton-model gebruik gemaak om hierdie probleem numeries te ondersoek. Eerstens word die faseverskuiwing van die verstrooiingsproses van ’n golfpakkie vanaf ’n kinkoplossing asimptoties in die topologiese eenheidssektor bepaal. Vir hierdie doel word die tydafhanklike bewegingsvergelykings van die klassieke, nie-integreerbare 4-veldeteorie in (1+1) dimensionele ruimte-tyd opgelos. Twee beginkondisies word ondersoek: ’n golfpakkie in die triviale vakuum agtergrond asook in die kinkoplossing agtergrond. Tweedens ondersoek ons ook numeriese oplossings vir die kink-antikink wisselwerking binne die triviale topologiese sektor van dieselfde model. Hier vind ons dat die finale toestand van hierdie wisselwerkingsproses op ’n uiters sensitiewe wyse van die impaksnelheid afhang. Ons ondersoek gevolglik die numeriese oplossings vir die kink-antikink botsings in twee gebiede. Vir beginsnelhede onder die kritieke snelheid vc 0:26 sal die kink en antikink mekaar óf vernietig óf nie-elasties verstrooi. In teenstelling hiermee sal die kink-antikink altyd nie-elastiese verstrooiing ondergaan as die beginsnelheid die kritieke snelheid oorskry. Die aard van die verstrooiingsprosesse vir beginsnelhede bo en onder die kritieke snelheid is egter verskillend. Onder die kritieke snelheid sal die kink en antikink ’n n-bots proses (n 2) ondergaan voor hulle finaal van mekaar weg beweeg. Bo die kritieke snelheid sal die kink-antikink egter net ’n enkele botsing ondergaan en dan uitmekaar beweeg. Ons lewer ’n kwalitatiewe beskrywing vir die bons-effek tussen die kink en antikink wat deur vorige studies asook ons numeriese resultate gemotiveer word. Ons maak gebruik van ’n kollektiewe koördinaatstelsel om die dinamika van die kink-antikink in terme van twee vryheidsgrade te bestudeer. In hierdie gebied pas ons ook die ansatz vir die kink-antikink stelsel aan om relatiwistiese effekte in ag te neem. Ons vergelyk dan hierdie benadering met die oplossing van die volle sisteem. Die bespreking van hierdie sektor word afgesluit met ’n analise van die verstrooiingsdata vir die verstrooiing- en vernietingsprosesse van die kink-antikink. Derdens vergelyk ons die verstrooiingsdata vir die verstrooiing van ’n golfpakkie vanaf ’n kinkoplossing met die van die vernietigingsproses van die kink-antikink. Ons studie van die verskillende sektore laat ons dan toe om ’n vermoede te formuleer oor die geldigheid van kruissing-simmetrie binne die nie-integreerbare 4-model.
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Juršėnas, Rytis. "Algebrinis daugiadalelės trikdžių teorijos plėtojimas teorinėje atomo spektroskopijoje." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20101223_152955-40113.
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Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose.The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences.
15
Benishti, Nessi. "The AdS/CFT correspondence and symmetry breaking." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:eb83f36f-fc48-4b75-b328-ff10ace0c08e.
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In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Such short multiplets originate from the Kaluza-Klein compactification of eleven-dimensional supergravity on the corresponding Sasaki-Einstein seven-manifolds. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over the well-known Sasaki-Einstein space Q^111, which is a U(1) fibration over CP^1 x CP^1 x CP^1. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and M5 branes wrapping five-cycles in the Q^111 space. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We then study the implications of turning on a closed three-form with non-zero periods through torsion three cycles in the Sasaki-Einstein manifold. This three-form, otherwise known as torsion G-flux, non-trivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^1,2(CP^2), which is a S^3 bundle over CP^2. We then explain how the choice of M-theory circle in the background can result in exotic renormalization group flows in the dual field theory, and study this in detail for the Sasaki-Einstein manifold Y^1,2(CP^2). We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Sasaki-Einstein Q^222 example, which is a Z_2 orbifold of Q^111 in which the free Z_2 quotient is along the R-symmetry U(1) fibre. The holographic interpretation of such instantons is currently unclear. In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular vacuum expectation values, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the NS-NS B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold theory and the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries, and identify the expected Goldstone bosons and global strings in the infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries.
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Ashdown, M. A. J. "Geometric algebra, group theory and theoretical physics." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596181.
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This dissertation applies the language of geometric algebra to group theory and theoretical physics. Geometric algebra, which is introduced in Chapter 2, provides a natural extension of the concept of multiplication from real numbers to geometric objects such as line segments and planes. It is based on Clifford algebra and augmented by auxiliary definitions which give it a geometric interpretation. Since geometric algebra provides a natural encoding of the concepts of directed quantities, it has the potential to unify many of the disparate systems of notation that are used in mathematics. In Chapter 3, the properties of multilinear functions are investigated and the theory is developed to make them useful for formulating the representation of groups. It will be found that multilinear functions are more flexible than their tensor or matrix counterparts in traditional linear algebra. Multilinear functions can be classified according to the symmetry class of their arguments and their behaviour under the monogenic or harmonic decomposition. It is found that the previous definitions of monogenic and harmonic functions need some modification if they are to be defined consistently. Polynomial projection is also discussed, a technique that is useful in constructing non-linear functions from linear functions, an operation outside the scope of conventional linear algebra. In Chapter 4, multilinear functions are used to construct the irreducible representations of the three regular classes of classical groups; rotation groups, the special unitary and special linear group, and the symplectic group. In each case it is found that a decomposition must be applied to the multilinear functions in order to find the irreducible representations of the groups. For the representations of some of the groups this entails finding the harmonic or monogenic parts of the functions. The groups can be realised as subgroups of the spin group of some dimension and signature. However, geometric algebra provides such a rich algebraic structure that the representations of the groups can be realised in more than one way. In Chapter 7 a brief review is given of computer software for performing symbolic calculations with geometric algebra. A new software package which performs semi-symbolic manipulation of multivectors in spaces of any dimension and signature is presented.
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Wiseman, Robin D. "The Jahn-Teller effect in icosahedral symmetry : unexpected lie group symmetries and their exploitation." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299385.
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Kangwai, Riki Dale. "The analysis of symmetric structures using group representation theory." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/265422.
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Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.
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Ban, Shufang. "Nuclear symmetry energy and neutron-proton pair correlations in microscopic mean field theory." Doctoral thesis, Stockholm : Fysik Physics, Kungliga Tekniska högskolan, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4469.
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Hinczewski, Michael 1979. "Renormalization-group theory of correlated electron systems." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34392.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Vita.
Includes bibliographical references.
The thesis applies position-space renormalization-group theory to a variety of correlated electron systems, determining finite-temperature phase diagrams and thermodynamic properties for electron densities both at and away from half-filling. We begin by assessing the effectiveness of the Suzuki-Takano quantum decimation method on a d = 1 Hubbard model in an external magnetic field, where exact results for the specific heat, magnetic and charge susceptibilities are available at various electron densities. We find that our approach converges to the exact values at high temperature, and agrees well even at moderate-to-low temperatures. We then extend the decimation through the Migdal-Kadanoff procedure to a Hubbard model in d = 3. Phase diagrams are calculated for a range of Coulomb couplings, and two new "" phases are found for hole-dopings of 10 - 18% and 30 - 35%. The electron hopping strength renormalizes to infinity at the T phase sinks, possibly indicating superconductivity, an interpretation further supported by features of the specific heat. The next part turns to the tJ model in d = 3, where the phase was originally observed. In the vicinity of this phase we see a sharp peak in the superfluid weight, and a suppressed low temperature specific heat indicating gap formation. The doping dependence of the free carrier density is similar to that found experimentally in cuprate superconductors. Since strong anisotropy is a key aspect of high-T, materials, we also consider a d = 3 tJ model with distinct in-plane and out-of-plane couplings. We examine the evolution of the phase diagram as the interplane coupling is weakened, and find that the T phase persists even in the quasi-two-dimensional regime.
(cont.) The complex lamellar structure of antiferromagnetic and disordered phases that develops between the T phase and half-filling could be a sign of incommensurate spin ordering. While the pure d = 2 tJ model does not exhibit a phase, we see pre-signatures of it in the renormalization-group flows, and the phase becomes stabilized with a finite transition temperature upon the addition of even the smallest interplane coupling. The last part of the thesis looks at renormalization-group techniques for quenched random systems. As a preliminary step to dealing with disorder in the tJ model, we start with a simpler, yet currently important, classical system, testing a conjecture relating the locations of multicritical points on dual pairs of hierarchical lattice Ising spin glasses. Finally, we incorporate nonmagnetic impurities into the d = 3 tJ model. Small oncentrations of these impurities rapidly destroy the r phase and enhance antiferromagnetism, observations that have parallels in Zn-doped cuprates.
by Michael Hinczewski.
Ph.D.
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Chaudhary, Irfan Ullah 1970. "Applications of group theory to few-body physics." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/30157.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (leaves 257-262).
Over the past fifteen years, there have been persistent claims of anomalous nuclear reactions in condensed matter environments. A Unified Model [38] has been proposed to systematically account for most of these anomalies. However, all the work done so far has used simple scalar nuclear Hamiltonians. In this thesis, we develop the tools necessary to use a realistic nuclear Hamiltonian in the Unified Model. A natural way to include a realistic nuclear potential in the Unified Model is via the method of coupled-channel equations. The phenomenological nuclear interaction chosen is the Hamada-Johnston potential [40]. The major portion of the thesis is devoted to deriving the coupled-channel equations with explicit symmetry constraints for the Hamada-Johnston potential. A critical input in this derivation is the calculation of the matrix elements of the various channels. We develop a systematic method, based on group theory, for calculating matrix elements of few-body correlated spatial wavefunctions. This method can, in some sense, be considered a generalization of Racah's viewpoint [17] of calculating shell-model matrix elements. Towards the end, two related, but somewhat different topics are explored. Firstly, a simple phonon-coupled nuclear reaction, the photodisintegration of the deuteron, is investigated. While no observable results are computed, this work should be considered a first step in calculating the effects of the lattice on nuclear reactions. Secondly, Lie algebra theory is used to understand the coherent decay, from the highest symmetry state in N-level systems, in terms of the usual Dicke [21] algebra.
by Irfan Ullah Chaudhary.
Ph.D.
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Daykin, Adam C. "A TEM analysis of the Co//Si(111) system using bicrystallographic symmetry theory." Thesis, University of Liverpool, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316591.
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Ryssens, Wouter. "Symmetry breaking in nuclear mean-field models." Doctoral thesis, Universite Libre de Bruxelles, 2016. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/235692.
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Dans les années 1970, Vautherin et Brink ont effectué les premiers calculs auto-consistents du problème à N-corps nucléaire en utilisant une interaction de Skyrme. Aujourd’hui la méthode de la fonctionnelle de densité (EDF) ou la méthode champ-moyen est toujours utilisée à grande échelle pour étudier la structure nucléaire. Le premier point fort de cette méthode est sa simplicité computationnelle qui permet de l'appliquer dans l'entièreté de la charte nucléaire, des noyaux les plus légers aux éléments super lourds à plus que 250 nucléons. Depuis le début des années 1980, les initiales `BFH', représentant Paul Bonche, Hubert Flocard et Paul-Henri Heenen, ont signé un grand nombre des papiers depuis 1984. Ces trois scientifiques sont les auteurs de trois codes numériques iconiques EV8, CR8 et EV4. Des versions évoluées de ces codes sont toujours utilisées fréquemment aujourd’hui par des nombreux chercheurs. Au fil des années, deux désavantages de ces trois codes sont apparus. Le premier désavantage est lié à la physique: bien que EV8, EV4 et CR8 offrent à l'utilisateur accès à une variété de combinaisons de symétries conservées et brisées, un grand nombre n'est pas accessible. De plus en plus souvent, les applications traitant des noyaux exotiques demandent des calculs champ-moyen qui sont moins limités par les symétries imposées. Le deuxième désavantage est d'une nature plus pratique: le maintien au même niveau d'une combinaison de trois codes qui ont des buts comparables est difficile. Le projet de mon doctorat était de construire un code qui unifie et généralise les fonctionnalités de EV8, CR8 et EV4. Aujourd'hui MOCCa, un acronyme de MOdular Cranking Code, est capable de reproduire toutes les fonctionnalités des codes BFH. De plus, il est maintenant possible d'effectuer des calculs champ-moyen pour un nombre des combinaisons de symétries conservées et brisées, offrant un domaine d'applications énorme. Quatre symétries ont été toujours imposées dans les codes BFH, et sont maintenant toutes soumises au choix de l'utilisateur, qui peut les conserver où les briser indépendamment. Ceci résulte en 16 modes d'opération différents du code, dont tous ont des intérêts physiques pour décrire des phénomènes nucléaires. La déformation octupolaire du 224Ra et les bandes chirales du 138Nd sont des exemples récents d'intérêt expérimental, dont la description théorique est maintenant abordable avec un seul outil. Cet outil fait preuve d'une grande complexité: sur le plan physique, des méthodes ont été développées pour résoudre les équations du champ-moyen en l'absence des symétries facilitant le problème, tandis que sur le plan pratique, le traitement d'un nombre de degrés de liberté non-physiques a eté amelioré. La dernière partie de la thèse, la plus importante probablement du point de vue des futurs collaborateurs, est pour cette raison constituée d'un manuel d'utilisateur. Deux applications de la méthode sont ainsi présentées: la description des transitions de forme dans les isotopes de Radium et une étude de l'évolution des rayons de charge dans la chaîne isotopique du mercure démontrent la viabilité de la méthode.Option Physique du Doctorat en Sciences
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Hekmati, Pedram. "Group Extensions, Gerbes and Twisted K-theory." Licentiate thesis, Stockholm : Teoretisk fysik, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4654.
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Hössjer, Emil. "Generalized Abelian Gauge Theory & Generalized Global Symmetry." Thesis, Uppsala universitet, Teoretisk fysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-434474.
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We study Cheeger-Simons differential characters in order to define higher form U(1) gauge fields and their Wilson lines. We then go on to define generalized global symmetries. This is a topological formulation of symmetries which has interesting consequences when the charged operators extend through space. Our main source of such charged operators are the generalized Wilson lines. A higher form Noether theorem and a Ward identity are given for transformations of Wilson lines. As examples of quantum field theories with generalized symmetries we cover Sigma models, Maxwell theory and BF-theory. These are examples of Z, U(1) and Zn symmetries respectively. Finally we discuss spontaneous symmetry breaking for higher dimensional symmetries and a Goldstone theorem is provided. These massless Goldstone bosons are shown to have internal structure corresponding to non-zero spin. The photon is identified as the spin one Goldstone boson in QED. Our review of generalized symmetries is more formal than the ones in other papers. This makes various points explicit and leads to general selection rules. Many results of previous papers are reproduced in detail.
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Lin, Tongyan S. B. Massachusetts Institute of Technology. "Group theory predictions for B --> M₁M₂M₃." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40914.
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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.Includes bibliographical references (leaves 65-66).
The study of B meson decays to 3 pseudoscalar mesons MMM provides a promising arena for constraining CP violation from the Standard Model and searching for "new physics". In this thesis we derive decay amplitudes, rates, and CP asymmetries for B mesons decaying to MMM, in the limit of SU(2) isospin and in the limit of SU(3) quark flavor symmetry. Our results are classified according to the relative angular momentum of mesons in the final states. When all the mesons have relative even angular momentum, there are 56 decay channels expressed as linear combinations of 7 reduced matrix elements. There are also 7 reduced matrix elements for the 36 decay channels where all the mesons have relative odd angular momentum. These results imply relations between the decay amplitudes, including several isospin triangles for B --> MMM, analogous to the B --> [pi][pi] isospin triangle. We also derive sum rules for isospin triangle. We also derive sum rules for B --> MMM, which give approximate SU(2) relations among branching ratios and CP asymmetries.
by Tongyan Lin.
S.B.
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George, Timothy Edward. "Symmetric representation of elements of finite groups." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.
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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.
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Barsegov, Valeri Abulevich. "Quantum decoherence and time symmetry breaking : quantum-classical correspondence in non-adiabatic transitions /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004212.
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Cassart, Delphine. "Optimal tests for symmetry." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210693.
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Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétrique localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour trois modèles d'asymétrie. La construction de modèles d'asymétrie est un sujet de recherche qui a connu un grand développement ces dernières années, et l'obtention des tests optimaux (pour trois modèles différents) est une étape essentielle en vue de leur mise en application.
Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance permet d'obtenir les procédures non-paramétriques.
Nous considérons dans ce travail deux classes de distributions univariées asymétriques, l'une fondée sur un développement d'Edgeworth (décrit dans le Chapitre 1), et l'autre construite en utilisant un paramètre d'échelle différent pour les valeurs positives et négatives (le modèle de Fechner, décrit dans le Chapitre 2).
Le modèle d'asymétrie elliptique étudié dans le dernier chapitre est une généralisation multivariée du modèle du Chapitre 2.
Pour chacun de ces modèles, nous proposons de tester l'hypothèse de symétrie par rapport à un centre fixé, puis par rapport à un centre non spécifié.
Après avoir décrit le modèle pour lequel nous construisons les procédures optimales, nous obtenons la propriété de normalité locale asymptotique. A partir de ce résultat, nous sommes capable de construire les tests paramétriques localement et asymptotiquement optimaux. Ces tests ne sont toutefois valides que si la densité sous-jacente f est correctement spécifiée. Ils ont donc le mérite de déterminer les bornes d'efficacité paramétrique, mais sont difficilement applicables.
Nous adaptons donc ces tests afin de pouvoir tester les hypothèses de symétrie par rapport à un centre fixé ou non, lorsque la densité sous-jacente est considérée comme un paramètre de nuisance.
Les tests que nous obtenons restent localement et asymptotiquement optimaux sous f, mais restent valides sous une large classe de densités.
A partir des propriétés d'invariance du sous-modèle identifié par l'hypothèse nulle, nous obtenons les tests de rangs signés localement et asymptotiquement optimaux sous f, et valide sous une vaste classe de densité. Nous présentons en particulier, les tests fondés sur les scores normaux (ou tests de van der Waerden), qui sont optimaux sous des hypothèses Gaussiennes, tout en étant valides si cette hypothèse n'est pas vérifiée.
Afin de comparer les performances des tests paramétriques et non paramétriques présentés, nous calculons les efficacités asymptotiques relatives des tests non paramétriques par rapport aux tests pseudo-Gaussiens, sous une vaste classe de densités non-Gaussiennes, et nous proposons quelques simulations.
Doctorat en sciences, Orientation statistique
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Bott, Christopher James. "Mirror Symmetry for K3 Surfaces with Non-symplectic Automorphism." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7456.
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Mirror symmetry is the phenomenon, originally discovered by physicists, that Calabi-Yau manifolds come in dual pairs, with each member of the pair producing the same physics. Mathematicians studying enumerative geometry became interested in mirror symmetry around 1990, and since then, mirror symmetry has become a major research topic in pure mathematics. One important problem in mirror symmetry is that there may be several ways to construct a mirror dual for a Calabi-Yau manifold. Hence it is a natural question to ask: when two different mirror symmetry constructions apply, do they agree?We specifically consider two mirror symmetry constructions for K3 surfaces known as BHK and LPK3 mirror symmetry. BHK mirror symmetry was inspired by the LandauGinzburg/Calabi-Yau correspondence, while LPK3 mirror symmetry is more classical. In particular, for algebraic K3 surfaces with a purely non-symplectic automorphism of order n, we ask if these two constructions agree. Results of Artebani Boissi`ere-Sarti originally showed that they agree when n = 2, and more recently Comparin-Lyon-Priddis-Suggs showed that they agree when n is prime. However, the n being composite case required more sophisticated methods. Whenever n is not divisible by four (or n = 16), this problem was solved by Comparin and Priddis by studying the associated lattice theory more carefully. In this thesis, we complete the remaining case of the problem when n is divisible by four by finding new isomorphisms and deformations of the K3 surfaces in question, develop new computational methods, and use these results to complete the investigation, thereby showing that the BHK and LPK3 mirror symmetry constructions also agree when n is composite.
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Mukai, Daichi. "Mirror symmetry of nonabelian Landau-Ginzburg orbifolds with loop type potentials." Kyoto University, 2020. http://hdl.handle.net/2433/253068.
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Tighe, John Francis. "Derivative expansions of the exact renormalisation group and SU(NN) gauge theory." Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368120.
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Hackett-Jones, E. J. "The role of chiral symmetry in extrapolations of lattice QCD results to the physical regime /." Title page, contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09SM/09smh121.pdf.
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Richardson, Andrew Stephen. "Topics in mode conversion theory and the group theoretical foundations of path integrals." W&M ScholarWorks, 2008. https://scholarworks.wm.edu/etd/1539623526.
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This dissertation reports research about the phase space perspective for solving wave problems, with particular emphasis on the phenomenon of mode conversion in multicomponent wave systems, and the mathematics which underlie the phase space perspective. Part I of this dissertation gives a review of the phase space theory of resonant mode conversion. We describe how the WKB approximation is related to geometrical structures in phase space, and how in particular ray-tracing algorithms can be used to construct the WKB solution. We further review how to analyze the phenomena of mode conversion from the phase space perspective. By making an expansion of the dispersion matrix about the mode conversion point in phase space, a local coupled wave equation is obtained. The solution of this local problem then provides a way to asymptotically match the WKB solutions on either side of the mode conversion region. We describe this theory in the context of a pedagogical example; that of a pair of coupled harmonic oscillators undergoing resonant conversion. Lastly, we present new higher order corrections to the local solution for the mode conversion problem which allow better asymptotic matching to the WKB solutions. The phase space tools used in Part I rely on the Weyl symbol calculus, which gives a way to relate operators to functions on phase space. In Part II of this dissertation, we explore the mathematical foundations of the theory of symbols. We first review the theory of representations of groups, and the concept of a group Fourier transform. The Fourier transform for commutative groups gives the ordinary transform, while the Fourier transform for non-commutative groups relates operators to functions on the group. We go on to present the group theoretical formulation of symbols, as developed recently by Zobin. This defines the symbol of an operator in terms of a double Fourier transform on a non-commutative group. We give examples of this new type of symbol, using the discrete Beisenberg-Wey1 group to construct the symbol of a matrix. We then go on to show how the path integral arises when calculating the symbol of a function of an operator. We also show how the phase space and configuration space path integrals arise when considering reductions of the regular representation of the Heisenberg-Wey1 group to the primary representations and irreducible representations, respectively. We also show how the path integral can be interpreted as a Fourier transform on the space of measures, opening up the possibility of using tools from statistical mechanics (such as maximum entropy techniques) to analyze the path integral. We conclude with a survey of ideas for future research and describe several potential applications of this group theoretical perspective to problems in mode conversion.
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Lin, Ting. "Poincaré-invariant three-nucleon scattering." Ohio : Ohio University, 2008. http://www.ohiolink.edu/etd/view.cgi?ohiou1210773278.
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Johnson, Jared Drew. "An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2793.
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Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz [10]. We also review the relevant parts of the constructions.
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Niyongabo, Prime. "Bound and free excitons in ZnO : optical selection rules in the absence and presence of time reversal symmetry." Diss., Pretoria : [s. n.], 2009. http://upetd.up.ac.za/thesis/available/etd-11292009-192654/.
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Chen, Long. "A ultraviolet complete large N thermal QCD model: renormalization group flow and mesonic spectra." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119566.
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The large N thermal Quantum Chromodynamics (QCD) that we study here is a generalization of SU(3) QCD with two gauge groups at high energy scales, i.e. in the ultraviolet (UV). Both gauge groups are related to N as SU(N)×SU(kN) with k < 1. In our construction, we have a model that has a complete UV description, as well as a low energy, i.e. infrared (IR), behaviour that mimicks that of QCD. Our model has three regions. The IR region is the well known cascading model with extensions to include favours. The two gauge groups of this theory reduce to a single SU(kN) group which then confines. The UV region uses congurations from type IIB string theory on the conifold to describe the dynamics. The intermediate region smoothly connects the two, i.e. the UV and the IR, so that we have a complete model for all energy scales. All regions are related to the gauge theory by gauge/gravity duality. In particular, we analyze the renormalization group (RG) flow of the gauge coupling in the effective field theory. We see that it asymptotically approaches a constant at high energies and flows toward permanent confinement as energy scale decreases. In the IR, we obtain the mesonic spectrum by compactifying extra dimensions and analyzing the wave functions in Minkowski space-time.Cette these etudies la limit N -> ∞ de la theorie chromodynamique quantique avec les deux groupes de jauge SU(N)×SU(kN) avec k < 1. Un modele est popose pour donner un description complete a la fois dans le regime ultraviolet(UV) et infrarouge(IR). Le regime IR concorde avec celui d'un modele de cascade, qui reduit de seule groupe de jaude SU(N) puis confine, tandis que le regime UV correspond a la theorie des cordes de type IIB sur conifold. Le regime UV possede alors une dualite de supergravite/jauge s'inscritvant dans la correspondance AdS/CFT. Dans le regime intermediere, notre molele connecte de maniere reguliere entre IR et UV. Le group de renormalization de la theorie effective est ensuite analyse. Nous comparons les resultats experimentaux en spectre du meson de notre modele das le regime IR.
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Herquet, Michel. "A two-Higgs-doublet model : from twisted theory to LHC phenomenology." Université catholique de Louvain, 2008. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-08212008-163854/.
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At the dawn of the Large Hadron Collider era, the Brout-Englert-Higgs mechanism remains the most appealing theoretical explanation of the electroweak symmetry breaking, despite the fact that the associated fundamental scalar boson has escaped any direct detection attempt. In this thesis, we consider a particular extension of the minimal Brout-Englert-Higgs scalar sector implemented in the Standard Model of strong and electroweak interactions. This extension, which is a specific, "twisted", realisation of the generic two-Higgs-doublet model, is motivated by a relative phase in the definition of the phenomenologically successful CP and custodial symmetries. Considering extensively various theoretical, indirect and direct constraints, this model appears as a viable alternative to more conventional scenarios like supersymmetric models, and gives grounds to largely unexplored possibilities of exotic scalar signatures at present and future collider experiments.
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Seyedi, Shila Seyedi. "QFT and Spontaneous Symmetry Breaking." Thesis, Uppsala universitet, Teoretisk fysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-425891.
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The aim of this project is to understand the structure of the Standard Model of the particle physics. Therefore quantum field theories (QFT) are studied in the both cases of abelian and non-abelian gauge theories i.e. quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak interaction are reviewed. The solution to the mass problem arising in these theories i.e. spontaneous symmetry breaking is also studied.Syftet med detta projekt är att förstå strukturen för partikelfysikens standardmodell. Därför studeras kvantfältsteorier (QFT) i båda fallen av abelska och icke-abelska gaugeteorier, dvs kvantelektrodynamik (QED), kvantkromodynamik (QCD) och elektrosvag växelverkan granskas. Lösningen på massproblemet som uppstår i dessa teorier, dvs. spontant symmetribrott studeras också.
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Ramanan, Sunethra. "Investigations of the renormalization group approach to the nucleon-nucleon interaction." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1173106852.
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SADE, MARTIN CHARLES. "VARIATIONAL PRINCIPLES FOR FIELD VARIABLES SUBJECT TO GROUP ACTIONS (GAUGE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188075.
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This dissertation is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables transform as type (0,1) tensor fields on M and are denoted by ψ(h)ᵅ (h = 1, ..., n = dim M, α = 1, ..., r = dim G). The dependence of ψ(h)ᵅ on the coordinates of G is given by a generalized gauge transformation that depends on a local map h:M → G. The requirement that a Lagrangian that is defined in terms of these field variables be independent of the coordinates of G and the choice of the map h endows G with a local Lie group structure. The class of Lagrangians that exhibits this type of invariance may be characterized by three invariance identities. These identities, together with an arbitrary solution of a system of partial differential equations, may be used to define field strengths associated with the ψ(h)ᵅ as well as connection and curvature forms on M. The former may be used to express the Euler-Lagrange equations in a particularly simple form. An energy-momentum tensor may also be defined in the usual manner; however additional conditions must be imposed in order to guarantee the existance of conservation laws resulting from this tensor. The above analysis may be repeated for the case that the field variables behave as type (0,2) tensor fields under coordinate transformations on M. For these field variables, the Euler-Lagrange expressions may be expressed as a product of a covariant divergence with the components λʰ of a type (1,0) vector field on M. An unexpected consequence of this construction is the fact that the Euler-Lagrange equations that result for the vector field λʰ are satisfied whenever the Euler-Lagrange equations associated with the field variables are satisfied.
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Dong, Bin. "Modal Analysis of General Cyclically Symmetric Systems with Applications to Multi-Stage Structures." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102605.
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This work investigates the modal properties of general cyclically symmetric systems and the multi-stage systems with cyclically symmetric stages. The work generalizes the modal properties of engineering applications, such as planetary gears, centrifugal pendulum vibration absorber (CPVA) systems, multi-stage planetary gears, etc., and provides methods to improve the computational efficiency to numerically solve the system modes when cyclically symmetric structures exist.
Modal properties of cyclically symmetric systems with vibrating central components as three-dimensional rigid bodies are studied without any assumptions on the system matrix symmetries: asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of such a cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem,all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each mode type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure.
Group theory is applied to further generalize the modal properties of cyclically symmetric systems when both rigid-body and compliant central components exist, such as planetary gears with an elastic continuum ring gear. The group theory for symmetry groups is introduced, and the group-theory-based modal analysis does not rely on any knowledge of the properties of system matrices in system equations of motion. The three types of modes (substructure modes, translational-tilting modes, and rotational-axial modes) are characterized by specific rigid-body central component modal defections, substructure phase relations, and nodal diameter components of compliant central components. The general formulation of reduced eigenvalue problems for each mode type is obtained through group-theory-based method, and it applies to discrete, continuous, or hybrid discrete-continuous cyclically symmetric systems. The group-theory-based modal analysis also applies to systems with other symmetry types.
The group-theory-based modal analysis is generalized to analyze the multi-stage systems that are composed of symmetric stages coupled through the motions of rigid-body central components. The proposed group-theory-based modal analysis applies to multi-stage systems with cyclically symmetric stages, such as multi-stage planetary gears and CPVA systems with multiple groups of absorbers. The method also applies to multi-stage systems with component stages that have different types of symmetry. For a multi-stage system with symmetric stages, a unitary transformation matrix can be built through an algorithmic and computationally inexpensive procedure. The obtained unitary transformation matrix provides the foundation to analyze the modal properties based on the principles of group-theory-based modal analysis. For general multi-stage systems with symmetric component stages, the vibration modes are classified into two general types, single-stage substructure modes and overall modes, according to the non-zero modal deflections in each component stage. Reduced eigenvalue problems for each mode type are formulated to reduce the computational cost for eigensolutions.
Finite element models of multi-stage bladed disk assemblies consist of multiple cyclically symmetric bladed disks that are coupled through the boundary nodes at the inter-stage interface. To improve the computational efficiency of calculating the full system modes, a numerical method is proposed by combination of the multi-stage cyclic symmetry reduction method and the subspace iteration method. Compared to the multi-stage cyclic symmetry reduction method, the proposed method improves the accuracy of obtained eigensolutions through an iterative process that is derived from the subspace iteration method. Based on the cyclic symmetry in each component stage of bladed disk, the proposed iterative method that can be performed using single stage sector models only, instead of using matrix operators for the full multi-stage bladed disks. Parallel computations can be performed in the proposed iterative method, and the computational speed for eigensolutions can be increased significantly.Doctor of Philosophy
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Zhou, Ye. "Renormalization group theory technique and subgrid scale closure for fluid and plasma turbulence." W&M ScholarWorks, 1987. https://scholarworks.wm.edu/etd/1539623774.
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Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term.;Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the {dollar}\epsilon{dollar} - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite {dollar}\epsilon{dollar}, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
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Xu, Guang-Hui. "Exploratory studies of group theoretic methods in atomic physics." Scholarly Commons, 1989. https://scholarlycommons.pacific.edu/uop_etds/2189.
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The properties of a physical system are determined by its equation of motion, and every such equation admits one-parameter groups which keep the equation invariant. Thus, for a particular system, if one can find the generator of a one-parameter group which keeps the equation and some further function or functional invariant, then one can change this system into others by changing the parameter, while keeping some properties constant. In this way, one can tell why different systems have some common properties. More importantly, one can use this method to find relationships between the physical properties of different systems.
In the next section, we will illustrate the group theoretic approach by applying it to systems of two coupled oscillators and the hydrogen molecular ion. In section III of this thesis, we will investigate the helium atom system, considering both classical and quantum cases. In the quantum case our attention will be concentrated on the Schrodinger equation in matrix form. We will use a finite set of wavefunctions as our basis. Hence the results obtained will be approximate.
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Robinson, Matthew Brandon Cleaver Gerald B. "Towards a systematic investigation of weakly coupled free fermionic heterotic string gauge group statistics." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5358.
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Foreman, Samuel Alfred. "Learning better physics: a machine learning approach to lattice gauge theory." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6944.
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In this work we explore how lattice gauge theory stands to benefit from new developments in machine learning, and look at two specific examples that illustrate this point. We begin with a brief overview of selected topics in machine learning for those who may be unfamiliar, and provide a simple example that helps to show how these ideas are carried out in practice.
After providing the relevant background information, we then introduce an example of renormalization group (RG) transformations, inspired by the tensor RG, that can be used for arbitrary image sets, and look at applying this idea to equilibrium configurations of the two-dimensional Ising model.
The second main idea presented in this thesis involves using machine learning to improve the efficiency of Markov Chain Monte Carlo (MCMC) methods. Explicitly, we describe a new technique for performing Hamiltonian Monte Carlo (HMC) simulations using an alternative leapfrog integrator that is parameterized by weights in a neural network. This work is based on the L2HMC ('Learning to Hamiltonian Monte Carlo') algorithm introduced in [1].
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Mantke, Wolfgang Johann. "Picture independent quantum action principle." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29850.
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Magini, Marcio. "Análise de simetrias nos grupos do tipo Dm usando conceitos de sistemas dinâmicos." Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-10092008-105333/.
Full textAbstract:
O entendimento de quebra espontânea de simetria é um problema importante para o estudo de fenômenos na evolução de sistemas abertos, tanto em física quanto em química, como também na biologia. Aqui estudamos um método a mais para este tipo de análise, usando conceitos de sistemas dinâmicos com simetria. O sistema dinâmico escolhido é discreto, isto é, realizado por iteração de um difeomorfismo equivariante sob a ação de um grupo compacto, neste caso um grupo finito do tipo Dm. Especificamente, investigamos o comportamento de atratores caóticos sob a variação dos parâmetros.The understanding of spontaneous symmetry breaking is an important problem in the study of phenomena in the evolution of open systems, in physics and chemistry as well as in biology. Here we study another method for this kind of analysis, using concepts from dynamical systems with symmetry. The chosen dynamical system is discrete, that is, realized by iteration of an equivariant diffeomorphism under the action of a compact group, in this case one of the finite groups of type Dm. Specifically, we investigate the behavior of chaotic attractors under variation of the parameters.
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Zou, Haiyuan. "Tensor renormalization group methods for spin and gauge models." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1420.
Full textAbstract:
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.