Дисертації з теми "Algebraic quantum theory"
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Comeau, Marc A. "Premonoidal *-Categories and Algebraic Quantum Field Theory." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/22652.
Повний текст джерелаHart, A. C. D. "An algebraic approach to bound state quantum field theory." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233666.
Повний текст джерелаAlcántara, Bode Julio, and J. Yngvason. "Algebraic quantum field theory and noncommutative moment problems I." Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/96072.
Повний текст джерелаLang, Benjamin. "Universal constructions in algebraic and locally covariant quantum field theory." Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/8019/.
Повний текст джерелаNyman, Adam. "The geometry of points on quantum projectivizations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5727.
Повний текст джерелаCooney, Nicholas. "Quantum multiplicative hypertoric varieties and localization." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2.
Повний текст джерелаLu, Weiyun. "Topics in Many-valued and Quantum Algebraic Logic." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35173.
Повний текст джерелаSolanki, Vinesh. "Zariski structures in noncommutative algebraic geometry and representation theory." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45.
Повний текст джерелаBRAGA, DE GOES E. VASCONCELLOS JOAO. "Thermal equilibrium states in perturbative Algebraic Quantum Field Theory in relation to Thermal Field Theory." Doctoral thesis, Università degli studi di Genova, 2019. http://hdl.handle.net/11567/979745.
Повний текст джерелаFALDINO, FEDERICO MARIA. "Facets of Non-Equilibrium in Perturbative Quantum Field Theory : an Algebraic Approach." Doctoral thesis, Università degli studi di Genova, 2018. http://hdl.handle.net/11567/933558.
Повний текст джерелаVan, De Ven Christiaan Jozef Farielda. "Quantum Systems and their Classical Limit A C*- Algebraic Approach." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/324358.
Повний текст джерелаRoquefeuil, Alexis. "Confluence of quantum K-theory to quantum cohomology for projective spaces." Thesis, Angers, 2019. http://www.theses.fr/2019ANGE0019/document.
Повний текст джерелаIn algebraic geometry, Gromov— Witten invariants are enumerative invariants that count the number of complex curves in a smooth projective variety satisfying some incidence conditions. In 2001, A. Givental and Y.P. Lee defined new invariants, called Ktheoretical Gromov—Witten invariants. These invariants are obtained by replacing cohomological objects used in the definition of the usual Gromov—Witten invariants by their Ktheoretical analogues. Then, an essential question is to understand how these two theories are related. In 2013, Iritani-Givental- Milanov-Tonita show that K-theoretical Gromov—Witten invariants can be embedded in a function which satisfies a q-difference equation. In general, these functional equations verify a property called “confluence”, which guarantees that we can degenerate these equations to obtain a differential equation. In this thesis, we propose to compare our two Gromov—Witten theories through the confluence of q-difference equations. We show that, in the case of complex projective spaces, this property can be adapted to degenerate Ktheoretical invariants into their cohomological analogues. More precisely, we show that theconfluence of Givental’s small K-theoretical Jfunction produces its cohomological analogue after applying the Chern character
SURIANO, LUCA. "A Quantum distance for noncommutative measure spaces and an application to quantum field theory." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/1326.
Повний текст джерелаIn the first part of this dissertation, we study a pointed version of Rieffel's quantum Gromov-Hausdorff topology for compact quantum metric spaces (i.e, order-unit spaces with a Lipschitz-like seminorm inducing a distance on the space of positive normalized linear functionals which metrizes the w*-topology). In particular, in analogy with Gromov's notion of metric tangent cone at a point of an (abstract) proper metric space, we propose a similar construction for (compact) quantum metric spaces, based on a suitable procedure of rescaling the Lipschitz seminorm on a given quantum metric space. As a result, we get a quantum analogue of the Gromov tangent cone, which extends the classical (say, commutative) construction. As a case study, we apply this procedure to the two-dimensional noncommutative torus, and we obtain what we call a noncommutative solenoid. In the second part, we introduce a quantum distance on the set of dual Lip-von Neumann algebras (i.e., vN algebras with a dual Lip-norm which metrizes the w*-topology on bounded subset). As for the other G.-H. distances (classical or quantum), this dual quantum Gromov-Hausdorff (pseudo-)distance turns out to be a true distance on the (Lip-)isometry classes of Lip-vN algebras. We give also a precompactness criterion, relating the limit of a (strongly) uniform sequence of Lip-vN algebras to the (restricted) ultraproduct, over an ultrafilter, of the same sequence. As an application, we apply this construction to the study of the Buchholz-Verch scaling limit theory of a local net of (algebras of) observables in the algebraic quantum field theory framework, showing that the two approaches lead to the same result for the (real scalar) free field model.
Thiang, Guo Chuan. "Topological phases of matter, symmetries, and K-theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:53b10289-8b59-46c2-a0e9-5a5fb77aa2a2.
Повний текст джерелаRosca, Georgiana-Miruna. "On algebraic variants of Learning With Errors." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEN063.
Повний текст джерелаLattice-based cryptography relies in great parts on the use of the Learning With Errors (LWE) problemas hardness foundation. This problem is at least as hard as standard worst-case lattice problems, but the primitives based on it usually have big key sizes and slow algorithms. Polynomial Learning With Errors (PLWE), dual Ring Learning With Errors (dual-RLWE) and primal Ring Learning WithErrors (primal-RLWE) are variants of LWE which make use of extra algebraic structures in order to fix the above drawbacks. The PLWE problem is parameterized by a polynomial f, while dual-RLWE andprimal-RLWE are defined using the ring of integers of a number field. These problems, which we call algebraic, also enjoy reductions from worst-case lattice problems, but in their case, the lattices involved belong to diverse restricted classes. In this thesis, we study relationships between algebraic variants of LWE.We first show that for many defining polynomials, there exist (non-uniform) reductions betweendual-RLWE, primal-RLWE and PLWE that incur limited parameter losses. These results could be interpretedas a strong evidence that these problems are qualitatively equivalent.Then we introduce a new algebraic variant of LWE, Middle-Product Learning With Errors (MP-LWE). We show that this problem is at least as hard as PLWE for many defining polynomials f. As a consequence,any cryptographic system based on MP-LWE remains secure as long as one of these PLWE instances remains hard to solve.Finally, we illustrate the cryptographic relevance of MP-LWE by building a public-key encryption scheme and a digital signature scheme that are proved secure under the MP-LWE hardness assumption
PUERTO, AUBEL ADRIAN. "Algebraic Structures for the Analysis of Distributability of Elementary Systems and their Processes." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2019. http://hdl.handle.net/10281/241253.
Повний текст джерелаThis work studies systems, and the processes they execute, in the way they can be distributed. To this aim, the central notion is that when a system is distributed, a remote observation requires an exchange of information from the different locations of the system. This approach is characterised by the fact that handshaking is the basic mode of interaction. The chosen formalisms are taken in the framework Petri net theory. Elemen- tary net systems, and condition/event net systems provide specifications for the systems. Causal nets and partially ordered sets allow for modelling processes. With these last formalisations, the state of the art provides a notion of subpro- cesses that can be structured so as to carry information on how a process can be distributed. This structure is formalised as an orthomodular lattice. This work shows that the minimal non trivial elements of this lattice, the minimal subprocesses, can be ordered so as to provide an abstraction of the process. The nature of this notion of subprocess permits to show that this abstraction depicts the localities of the process, parts of the process which can run independently from each other. The behaviour of elementary, and condition/event net systems, is modelled with labelled transition systems. This work adheres to an interpretation of the set of elementary regions, as the one of locally observable properties of the sys- tem, motivated by elementary net synthesis. According to this interpretation, elementary regions represent a suitable specification of the available infrastruc- ture on which to distribute a system. The state of the art shows that the set of regions of an elementary, or condition/event system, forms an orthomodular poset, and a way to retrieve a canonical labelled transition system such that all regions of the orthomodular poset are also regions of it. The question of whether this canonical transition system has more regions than the specified ones is an open problem. The canonical transition system is the largest one can obtain from an orthomodular poset, in the sense that systems complying with the specification, can be found as subsystems of it. However, not all its subsystems display the same regional structure. This work presents a sufficient condition for this to happen. This is achieved by providing a structure to the set of events, or labels, of the canonical system, which reflects concurrency. An orthomodular poset is called stable when it is isomorphic to the set of regions of its canonical transition system. The state of the art shows that when the first poset is of a given class, it embeds in the second. It is conjectured that all posets that arise as the set of elementary regions of an elementary system, regional posets, are stable. This work provides a condition necessary for an orthomodular poset to be regional, and shows that when it holds, the embedding is strong. Not every embedding is strong, but all isomorphisms are, in particular, strong embeddings. This result implies that the embedding maps minimal regions to minimal regions.
Juer, Rosalinda. "1 + 1 dimensional cobordism categories and invertible TQFT for Klein surfaces." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b9a8fc3b-4abd-49a1-b47c-c33f919a95ef.
Повний текст джерелаAlmeida, Ricardo Costa de. "Topological order in three-dimensional systems and 2-gauge symmetry." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-05122017-094209/.
Повний текст джерелаOrdem topológica é um novo paradigma para fases quânticas da matéria desenvolvido para explicar transições de fase que não se encaixam no esquema de classificação de fases da matéria por quebra de simetria. Estas fases são caracterizadas por padrões de emaranhamento que levam a uma degenerescência de estado fundamental topológica e a excitações anyonicas. Uma abordagem comum para o estudo de tais fases em sistemas bidimensionais é através de modelos Hamiltonianos exatamente solúveis de rede como os modelos duplos quânticos e modelos de String-Nets. O primeiro pode ser entendido como a formulação Hamiltoniana de teorias de gauge na rede e, desta maneira, é definido por um group de gauge finito. Entretanto, pouco é conhecido a respeito de fases topológicas em sistemas tridimensionais. Motivado por isso nós desenvolvemos uma nova classe de modelos tridimensionais exatamente solúveis que vai alem de modelos duplos quânticos pelo uso de módulos cruzados finitos no lugar de grupos de gauge. Esta abordagem se baseia numa implementação em redes de teoria de 2-gauge para obter modelos com uma estrutura topológica mais rica. Nós construímos o modelos Hamiltoniano explicitamente e fornecemos uma demonstração rigorosa de que a degenerescência de estado fundamental é um invariante topológico e que os estados fundamentais só podem ser caracterizados por parâmetros de ordem não locais.
Diaz, Caro Alejandro. "Du typage vectoriel." Thesis, Grenoble, 2011. http://www.theses.fr/2011GRENM038/document.
Повний текст джерелаThe objective of this thesis is to develop a type theory for the linear-algebraic λ-calculus, an extension of λ-calculus motivated by quantum computing. This algebraic extension encompass all the terms of λ-calculus together with their linear combinations, so if t and r are two terms, so is α.t + β.r, with α and β being scalars from a given ring. The key idea and challenge of this thesis was to introduce a type system where the types, in the same way as the terms, form a vectorial space, providing the information about the structure of the normal form of the terms. This thesis presents the system Lineal, and also three intermediate systems, however interesting by themselves: Scalar, Additive and λCA, all of them with their subject reduction and strong normalisation proofs
Lechner, Gandalf. "On the construction of quantum field theories with factorizing S-matrices." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/lechner.
Повний текст джерелаSilva, Anderson Alves da. "Construção de uma teoria quântica dos campos topológica a partir do invariante de Kuperberg." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26102015-133218/.
Повний текст джерелаAbstract In this work we present in detail a construction of a topological quantum field theory (TQFT). We can define a TQFT as a symmetric monoidal functor from cobordism categories to category of vector spaces. In two dimension, we can give a complete description of cobordism categories and classify all TQFT\'s. In three dimension it is possible to extend some specific 3-manifold invariants and to construct a TQFT 3D. Our construction is based on the Kuperberg 3-manifold invariant which involves Heegaard diagrams and Hopf algebras. We start with the presentation of the Kuperberg invariant defined for every orientable compact 3-manifold without boundary. For each finite-dimensional Hopf algebra we can construct a invariant. Finally we presente the TQFT associated with the Kuperberg invariant. This is made using the fact that the Kuperberg invariant is defined like a sum of local weights in the same way as a partition function. The TQFT is constructed from the operators given by manifolds with boundary.
Javelle, Jérôme. "Cryptographie Quantique : Protocoles et Graphes." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM093/document.
Повний текст джерелаI want to realize an optimal theoretical model for quantum secret sharing protocols based on graph states. The main parameter of a threshold quantum secret sharing scheme is the size of the largest set of players that can not access the secret. Thus, my goal is to find a collection of protocols for which the value of this parameter is the smallest possible. I also study the links between quantum secret sharing protocols and families of curves in algebraic geometry
Schultka, Konrad. "Microlocal analyticity of Feynman integrals." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20161.
Повний текст джерелаWe give a rigorous construction of analytically regularized Feynman integrals in D-dimensional Minkowski space as meromorphic distributions in the external momenta, both in the momentum and parametric representation. We show that their pole structure is given by the usual power-counting formula and that their singular support is contained in a microlocal generalization of the alpha-Landau surfaces. As further applications, we give a construction of dimensionally regularized integrals in Minkowski space and prove discontinuity formula for parametric amplitudes.
Eltzner, Benjamin. "Local Thermal Equilibrium on Curved Spacetimes and Linear Cosmological Perturbation Theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-117472.
Повний текст джерелаIn dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft
Olbermann, Heiner. "Quantum field theory via vertex algebras." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/54994/.
Повний текст джерела
Ribeiro, Pedro Lauridsen. "Aspectos estruturais e dinâmicos da correspondência AdS/CFT: Uma abordagem rigorosa." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14012008-131931/.
Повний текст джерелаWe elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter\'s conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren\'s result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity\'s quantum theory. Among the obtained results, we quote: not only does the imposition of reasonably general conditions on bulk null geodesics (whose plausibility we justify through geometrical rigidity techniques) guarantee that our generalization is geometrically consistent with causality, but it also allows a ``holographic\'\' reconstruction of the bulk topology in the absence of horizons and singularities; the implementation of conformal symmetries in the boundary, which we explicitly associate to an intrinsically constructed family of bulk asymptotic isometries, have a purely asymptotic character and is dynamically attained through a process of return to equilibrium, given suitable boundary conditions at infinity; gravitational effects may cause obstructions to the reconstruction of the bulk quantum theory, either by making the latter trivial in sufficiently small regions or due to the existence of multiple inequivalent vacua, which on their turn lead to the existence of solitonic excitations localized around domain walls, similar to D-branes. The proofs make extensive use of global Lorentzian geometry. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions. (An English translation of the full text can be found at arXiv:0712.0401)
Campos, Lissa de Souza. "Os teoremas de singularidade valem se considerarmos efeitos quânticos?" Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-03122018-144411/.
Повний текст джерелаThere are two quantum loopholes in the Singularity Theorems of General Relativity: violations of the classical energy conditions and quantum fluctuations of the spacetime geometry. In this dissertation, we study the first loophole and approach Singularity Theorems through the energy condition. We review the algebraic approach of Quantum Field Theory for the Klein-Gordon field and, within it, we review the derivation of a quantum energy inequality for Hadamard states on globally hyperbolic spacetimes. However quantum energy inequalities cannot be directly applied to Singularity Theorems, we show that generalized Hawking and Penrose Theorems are proven considering weakened energy conditions inspired by them. Hence, Singularity Theorems do hold under subtle quantum effects. The question of whether interaction or backreaction effects could break them is still open; there are reasons to expect both answers.
Fernandes, Marco Cezar Barbosa. "Geometric algebras and the foundations of quantum theory." Thesis, Birkbeck (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283390.
Повний текст джерелаGordon, Iain. "Representation theory of quantised function algebras at roots of unity." Thesis, Connect to electronic version, 1998. http://hdl.handle.net/1905/177.
Повний текст джерелаSatchell, Marcel John Francis. "Geometric algebra & the quantum theory of fields." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708105.
Повний текст джерелаSomaroo, Shyamal Sewlal. "Applications of the geometric algebra to relativistic quantum theory." Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627593.
Повний текст джерелаBrzezinski, Tomasz. "Differential geometry of quantum groups and quantum fibre bundles." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321113.
Повний текст джерелаShiri-Garakani, Mohsen. "Finite Quantum Theory of the Harmonic Oscillator." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5078.
Повний текст джерелаSotelo-Campos, J. "An application of operator *-algebras to the theory of quantum measurement." Thesis, Open University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379797.
Повний текст джерелаKleeman, R. "Generalized quantization and colour algebras /." Title page, table of contents and abstract only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phk635.pdf.
Повний текст джерелаRubensson, Emanuel H. "Matrix Algebra for Quantum Chemistry." Doctoral thesis, Stockholm : Bioteknologi, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9447.
Повний текст джерелаLaugwitz, Robert. "Braided Hopf algebras, double constructions, and applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:ddcb459f-c3b4-40dd-9936-6bad6993ce8c.
Повний текст джерелаBittmann, Léa. "Quantum Grothendieck rings, cluster algebras and quantum affine category O." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC024.
Повний текст джерелаThe aim of this thesis is to construct and study some quantum Grothendieck ring structure for the category O of representations of the Borel subalgebra Uq(^b) of a quantum affine algebra Uq(^g). First of all, we focus on the construction of asymptotical standard modules, analogs in the context of the category O of the standard modules in the category of finite-dimensional Uq(^g)-modules. A construction of these modules is given in the case where the underlying simple Lie algebra g is sl2. Next, we define a new quantum torus, which extends the quantum torus containing the quantum Grothendieck ring of the category of finite-dimensional modules. In order todo this, we use notions linked to quantum cluster algebras. In the same spirit, we build a quantum cluster algebra structure on the quantum Grothendieck ring of a monoidal subcategory CZ of the category of finite-dimensional representations. With this quantum torus, we de_ne the quantum Grothendieck ring Kt(O+Z) of a subcategory O+Z of the category O as a quantum cluster algebra. Then, we prove that this quantum Grothendieck ring contains that of the category of finite-dimensional representation. This result is first shown directly in type A, and then in all simply-laced types using the quantum cluster algebra structure of Kt(CZ). Finally, we define (q,t)-characters for some remarkable infinite-dimensional simple representations in the category O+Z. This enables us to write t-deformed analogs of important relations in the classical Grothendieck ring of the category O, which are related to the corresponding quantum integrable systems
De, Buyl Sophie. "Kac-Moody Algebras in M-theory." Doctoral thesis, Universite Libre de Bruxelles, 2006. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210850.
Повний текст джерелаNous avons étudié la limite BKL dans le contexte des cosmologies homogènes en terme de billard einsteiniens. Notre analyse confirme la restauration du comportement chaotique du champ gravitationnel lorsque la métrique est non – diagonale, en toutes les dimensions D d’espace-temps telles que 4 En utilisant les propriétés des billards, nous avons déterminé la dimension maximale ainsi que le contenu en champs des théories de la gravitation qui, en D=3, se réduisent à la gravité couplée à une réalisation non linéaire du quotient G/K où G est un groupe de Lie simple non maximalement déployé et K son sous-groupe compact maximal. Les billards peuvent être de volume fini ou infini. Dans ce dernier cas, la dynamique asymptotique du champ de gravitation (et des dilatons) est chaotique. Si le billard est identifiable à la chambre fondamentale de Weyl d’une algèbre de Kac-Moody, le critère pour que la dynamique asymptotique soit chaotique est que l’algèbre de Kac-Moody soit hyperbolique. Nous avons identifié toutes les algèbres hyperboliques résultant d’une théorie de la gravitation couplée à des p-formes et des dilatons. Pour chacune de ces algèbres, nous avons écrit un Lagrangien en dimension maximale. On obtient des actions explicitement invariantes sous les groupes de Kac-Moody G++ (ou G+++) en copiant les modèles sigma décrivant un mouvement géodésique sur une variété homogène de type G++/K(G++) où K(G++) est le sous-groupe compact maximal de G++. Le lien entre cette construction et les théories de la gravitation couplée à des p-formes et dilatons n'est pas encore établi mais certaines connexions ont été mises en évidence. - Nous avons inclus les fermions dans les actions invariantes sous G++. De plus, nous nous sommes intéressés à vérifier la compatibilité des fermions avec les symétries cachées en D=3. Nous avons étudié le comportement des fermions la limite BKL dans le langage des billards. - Dans le cadre des théories invariantes sous G+++, les réflexions de Weyl peuvent s’interpréter comme des dualités entre théorie des cordes. Ces dualités peuvent changer la signature de l’espace-temps en des signatures exotiques ;nous avons obtenu toutes les signatures provenant ainsi d’une signature Lorentzienne.
Doctorat en sciences, Spécialisation physique
info:eu-repo/semantics/nonPublished
Wong, Ming Lai. "Q-Fourier transform, q-Heisenberg algebra and quantum group actions /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20WONG.
Повний текст джерелаSchopieray, Andrew. "Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity." Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22630.
Повний текст джерелаBoixeda, Alvarez Pablo. "Affine Springer fibers and the representation theory of small quantum groups and related algebras." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126920.
Повний текст джерелаCataloged from the official PDF of thesis.
Includes bibliographical references (pages 125-128).
This thesis deals with the connections of Geometry and Representation Theory. In particular we study the representation theory of small quantum groups and Frobenius kernels and the geometry of an equivalued affine Springer fiber Fl[subscript ts] for s a regular semisimple element. In Chapter 2 we relate the center of the small quantum group with the cohomology of the above affine Springer fiber. This includes joint work with Bezrukavnikov, Shan and Vaserot. In Chapter 3 we study the geometry of the affine Springer fiber and in particular understand the fixed points of a torus action contained in each component. In Chapter 4 we further have a collection of algebraic results on the representation theory of Frobenius kernels. In particular we state some results pointing towards some construction of certain partial Verma functors and we compute this in the case of SL₂. We also compute the center of Frobenius kernels in the case of SL₂ and state a conjecture on a possible inductive construction of the general center.
by Pablo Boixeda Alvarez.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
HILLIER, ROBIN. "Spectral triples and an index pairing for conformal quantum field theory." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/202295.
Повний текст джерелаLagro, Matthew Patrick. "A Perron-Frobenius Type of Theorem for Quantum Operations." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/339694.
Повний текст джерелаPh.D.
Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.
Temple University--Theses
Diemer, Tammo. "Conformal geometry, representation theory and linear fields." Bonn : Mathematisches Institut der Universität, 2004. http://catalog.hathitrust.org/api/volumes/oclc/62770144.html.
Повний текст джерелаKartsaklis, Dimitrios. "Compositional distributional semantics with compact closed categories and Frobenius algebras." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1f6647ef-4606-4b85-8f3b-c501818780f2.
Повний текст джерелаVougalter, Vitali. "Diamagnetic behavior of sums of Dirichlet eigenvalues." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28034.
Повний текст джерелаKatona, Gregory. "Field Theoretic Lagrangian From Off-Shell Supermultiplet Gauge Quotients." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5958.
Повний текст джерелаPh.D.
Doctorate
Physics
Sciences
Physics
Albouy, Olivier. "Discrete algebra and geometry applied to the Pauli group and mutually unbiased bases in quantum information theory." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00612229.
Повний текст джерелаRussell, Neil Eric. "Aspects of the symplectic and metric geometry of classical and quantum physics." Thesis, Rhodes University, 1993. http://hdl.handle.net/10962/d1005237.
Повний текст джерела