Tesis sobre el tema "Gauge theory on noncommutative spaces"
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Bizi, Nadir. "Semi-riemannian noncommutative geometry, gauge theory, and the standard model of particle physics". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS413/document.
Texto completoThe subject of this thesis is noncommutative geometry - more specifically spectral triples - and how it can be used to unify General Relativity with the Standard Model of particle physics. This unification has already been achieved with spectral triples for Riemannian manifolds. The main concern of this thesis is to generalize this construction to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition from Riemannian to semi-Riemannian manifolds. This entails a study of Clifford algebras for indefinite vector spaces and Spin structures on semi-Riemannian manifolds. An important consequence of this is the introduction of complex vector spaces of indefinite signature. These are the so-called Krein spaces, which will enable us to generalize spectral triples to indefinite spectral triples. In the second half of this thesis, we will apply the formalism of noncommutative differential forms to indefinite spectral triples to construct noncommutative gauge theories on Lorentzian spacetimes. We will then demonstrate how to recover the Standard Model
Meyer, Frank. "Gauge-Field Theories and Gravity on Noncommutative Spaces". Diss., lmu, 2006. http://nbn-resolving.de/urn:nbn:de:bvb:19-53357.
Texto completoBehr, Wolfgang. "Noncommutative Gauge Theory beyond the Canonical Case". Diss., lmu, 2005. http://nbn-resolving.de/urn:nbn:de:bvb:19-44251.
Texto completoMöller, Lutz. "Noncommutative gauge theory and the kappa-deformed spacetime". Diss., lmu, 2004. http://nbn-resolving.de/urn:nbn:de:bvb:19-23608.
Texto completoMielke, Thomas Martin. "Mapping spaces, configuration spaces and gauge theory". Thesis, University of Warwick, 1995. http://wrap.warwick.ac.uk/109201/.
Texto completoGrosse, Harald, Thomas Krajewski, Raimar Wulkenhaar y grosse@doppler thp univie ac at. "Renormalization of Noncommutative Yang-Mills Theories: A Simple Example". ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi914.ps.
Texto completoSykora, Andreas. "The application of star-products to noncommutative geometry and gauge theory". Diss., lmu, 2004. http://nbn-resolving.de/urn:nbn:de:bvb:19-28937.
Texto completoVolkholz, Jan. "Nonperturbative studies of quantum field theories on noncommutative spaces". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2007. http://dx.doi.org/10.18452/15712.
Texto completoThis work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore a scalar model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized scalar model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations.
Daemi, Aliakbar. "Symmetric Spaces and Knot Invariants from Gauge Theory". Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11563.
Texto completoMathematics
Sardis, Ioannis E. E. "Gluing maps, moduli spaces of connections and Donaldson invariants". Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263327.
Texto completoIvankov, Nikolay [Verfasser]. "Unbounded Bivariant K-theory and an Approach to Noncommutative Fréchet Spaces / Nicolay Ivankov". Bonn : Universitäts- und Landesbibliothek Bonn, 2011. http://d-nb.info/1016150652/34.
Texto completoSURIANO, 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.
Texto completoIn 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.
Nikoofard, Vahid. "Some considerations about field theories in commutative and noncommutative spaces". Universidade Federal de Juiz de Fora (UFJF), 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/3057.
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Esta tese é composta por assuntos distintos entre si de teorias quânticas de campos onde alguns deles são descritos em espaços não-comutativos (NC). Em primeiro lugar, analisamos a dinâmica de uma partícula livre sobre uma 2-esfera e através da dinâmica das suas equações de movimento, obtivemos as perturbações NCs neste espaço de fase. Este modelo sugere uma origem para o Zitterbewegung do elétron. Depois disso, consideramos umaversãoNCdasegundaleideNewtonparaestemodelo, quefoiobtidocomestecenário geométrico aplicado a este modelo. Em seguida, discutimos um formalismo alternativo relacionado à não-comutatividade chamado DFR onde o parâmetro NC é considerado uma coordenada e demonstramos exatamente que ela tem obrigatoriamente um momento conjugado neste espaço de fase DFR, diferentemente do que alguns autores da atual literatura sobre DFR afirmam. No próximo assunto, usando o formalismo de solda que, em poucaspalavras,colocapartículascomquiralidadesopostasnomesmomultipleto,soldamos algumas versões NCs de modelos bem conhecidos como modelos de Schwinger quirais e modelos (anti) auto duais no espaço-tempo de Minkowski estendido. Em outro assunto estudado aqui, também construímos a versão NC do modelo de Jackiw-Pi com um grupo de calibre arbitrário e usamos o mapeamento bem conhecido de Seiberg-Witten para obter este modelo NC em termos de variáveis comutativos. Finalmente, utilizamos o formalismo de campos e anticampos (ou método BV) para construir a ação de Batalin-Vilkovisky (BV) do modelo Jackiw-Pi estendido e após o prEntendiocedimento de fixação de calibre chegamos a uma ação completa, pronta para quantização.
This thesis is composed of distinct aspects of quantum field theories where some of them are described in noncommutative (NC) spaces. Firstly, we have analyzed the dynamics of a free particle over a 2-sphere and through the dynamics of the equations of motion we have derived its NC perturbations in the phase-space. This model suggests an origin for Zitterbewegung feature of the electron. After that we have considered the NC version of Newton’s second law for this model, which was obtained with the geometricalscenarioappliedtothismodel. Thenwehavediscussedtheso-calledDoplicher– Fredenhagen–Roberts (DFR) alternative formalism concerning noncommutativity where the NC parameter has a coordinate role and we showed exactly that it has a conjugated momentum in the DFR phase-space, differently of what some authors of the current DFR-literature claims. In the next issue, using the soldering formalism which, in few words, put opposite chiral particles in the same multiplet, we have soldered some NC versions of well known models like the chiral Schwinger model and (anti)self dual models in the extended Minkowski spacetime. Changing the subject, we have constructed the NC spacetime version of Jackiw-Pi model with an arbitrary gauge group and we used the well known Seiberg-Witten map to obtain the NC model expressed in terms of commutative variables. Finally, we have used the field-antifield (or BV method) formalism to construct the Batalin-Vilkovisky (BV) action of the extended Jackiw-Pi model and after the gauge fixing procedure we have arrived at a quantized-ready action for this model.
Sundin, Per. "Perturbative quantization of superstring theory in Anti de-Sitter spaces". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16320.
Texto completoIn this thesis we study superstring theory on AdS$_5\, \times\,$S$^5$, AdS$_3\,\times\,$S$^3$ and $\adsfour$. A shared feature of each theory is that their corresponding symmetry algebras allows for a decomposition under a $\mathbb{Z}_4$ grading. The grading can be realized through an automorphism which allows for a convenient construction of the string Lagrangians directly in terms of graded components. We adopt a uniform light-cone gauge and expand in a near plane wave limit, or equivalently, an expansion in transverse string coordinates. With a main focus on the two critical string theories, we perform a perturbative quantization up to quartic order in the number of fields. Each string theory is, through holographic descriptions, conjectured to be dual to lower dimensional gauge theories. The conjectures imply that the conformal dimensions of single trace operators in gauge theory should be equal to the energy of string states. What is more, through the use of integrable methods, one can write down a set of Bethe equations whose solutions encode the full spectral problem. One main theme of this thesis is to match the predictions of these equations, written in a language suitable for the light-cone gauge we employ, against explicit string theory calculations. We do this for a large class of string states and the perfect agreement we find lends strong support for the validity of the conjectures.
Johnston, Ann. "Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data". Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/4.
Texto completoBecker, Christian. "On the Riemannian geometry of Seiberg-Witten moduli spaces". Phd thesis, [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975744771.
Texto completoSundin, Per [Verfasser], Sergey [Akademischer Betreuer] Frolov, Stefan [Akademischer Betreuer] Theisen y Peter [Akademischer Betreuer] Uwer. "Perturbative quantization of superstring theory in Anti de-Sitter spaces : integrability in gauge / string dualities / Per Sundin. Gutachter: Sergey Frolov ; Stefan Theisen ; Peter Uwer". Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://d-nb.info/1015081290/34.
Texto completoKailasvuori, Janik. "Quasiparticles in the Quantum Hall Effect". Doctoral thesis, Stockholm : Department of Physics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1250.
Texto completoDe, Notariis Kevin. "Light hyperweak new gauge bosons from kinetic mixing in string models". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19491/.
Texto completoCazassus, Guillem. "Homologie instanton-symplectique : somme connexe, chirurgie de Dehn, et applications induites par cobordismes". Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30043/document.
Texto completoSymplectic instanton homology is an invariant for closed oriented three-manifolds, defined by Manolescu and Woodward, which conjecturally corresponds to a symplectic version of a variant of Floer's instanton homology. In this thesis we study the behaviour of this invariant under connected sum, Dehn surgery, and four-dimensional cobordisms. We prove a Künneth-type formula for the connected sum: let Y and Y' be two closed oriented three-manifolds, we show that the symplectic instanton homology of their connected sum is isomorphic to the direct sum of the tensor product of their symplectic instanton homology, and a shift of their torsion product. We define twisted versions of this homology, and then prove an analog of the Floer exact sequence, relating the invariants of a Dehn surgery triad. We use this exact sequence to compute the rank of the groups associated to branched double covers of quasi-alternating links, some plumbings of disc bundles over spheres, and some integral Dehn surgeries along certain knots. We then define invariants for four dimensional cobordisms as maps between the symplectic instanton homology of the two boundaries. We show that among the three morphisms in the surgery exact sequence, two are such maps, associated to the handle-attachment cobordisms. We also give a vanishing criteria for such maps associated to blow-ups
Chandra, Nitin. "Topics In Noncommutative Gauge Theories And Deformed Relativistic Theories". Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2468.
Texto completoMeyer, Frank [Verfasser]. "Gauge-field theories and gravity on noncommutative spaces / vorgelegt von Frank Meyer". 2006. http://d-nb.info/980449014/34.
Texto completoBehr, Wolfgang [Verfasser]. "Noncommutative gauge theory beyond the canonical case / vorgelegt von Wolfgang Behr". 2005. http://d-nb.info/97757055X/34.
Texto completoMarcillaud, de Goursac Axel [Verfasser]. "Noncommutative geometry, gauge theory and renormalization / vorgeelgt von Axel Marcillaud de Goursac". 2009. http://d-nb.info/1002113490/34.
Texto completoSykora, Andreas [Verfasser]. "The application of *-products to noncommutative geometry and gauge theory / Andreas Sykora". 2004. http://d-nb.info/974061336/34.
Texto completoMöller, Lutz [Verfasser]. "Noncommutative gauge theory and κ-deformed [kappa-deformed] spacetime / vorgelegt von Lutz Möller". 2004. http://d-nb.info/972021833/34.
Texto completoAlekseev, Vadim. "Noncommutative manifolds and Seiberg-Witten-equations". Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-B3ED-D.
Texto completo