Conformal Field Theories in Symplectic Manifolds

Detalhes bibliográficos
Autor(a) principal: Petronilo, Gustavo Xavier Antunes
Data de Publicação: 2024
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UnB
Texto Completo: http://repositorio2.unb.br/jspui/handle/10482/49527
Resumo: Tese (doutorado em Física) — Universidade de Brasília, Brasília, 2024.
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spelling Conformal Field Theories in Symplectic ManifoldsMecânica quânticaFunção de WignerTese (doutorado em Física) — Universidade de Brasília, Brasília, 2024.This work investigates the notion of a conformal group and derives a representation for symplectic quantum mechanics in the Galilean manifold, G, in a consistent manner using the Wigner function method. We study two non-Lorentzian conformal symmetries: the Conformal Carrollian group and the Sch¨odinger group. A symplectic Hilbert space is built and unitary operators representing translations and rotations are studied, whose generators fulfill the Lie algebra in G. The Schr¨odinger (Klein-Gordon-like) equation for the wave functions in phase space is derived from this representation, where the variables have the contents of position and linear momentum. By means of the Moyal product, wave functions are linked to the Wigner function, so symbolizing a quasi-amplitude of probability. We establish the explicitly covariant form of the Levy-Leblond (Dirac-like) equation in phase-space. In conclusion, we demonstrate how the five-dimensional phase space formalism and the standard formalism are equivalent. We next provide a solution that restores the standard (non-covariant) form of the Pauli-Schr¨odinger problem in phase space. We investigate the non-relativistic part of the Stefan-Boltzmann law and the Casimir effect for the spin 0 and spin 1/2 particles with thermofield dynamics, also within the framework of Galilean covariance.Instituto de Física (IF)Programa de Pós-Graduação em FísicaSantana, Ademir Eugênio deUlhoa, Sérgio CostaPetronilo, Gustavo Xavier Antunes2024-08-05T19:43:49Z2024-08-05T19:43:49Z2024-08-052024-03-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfPETRONITO, Gustavo Xavier Antunes. Conformal Field Theories in Symplectic Manifolds. 2024. 128 f. il. Tese (Doutorado em Física) — Universidade de Brasília, Brasília, 2024.http://repositorio2.unb.br/jspui/handle/10482/49527enginfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNB2024-08-05T19:44:37Zoai:repositorio.unb.br:10482/49527Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2024-08-05T19:44:37Repositório Institucional da UnB - Universidade de Brasília (UnB)false
dc.title.none.fl_str_mv Conformal Field Theories in Symplectic Manifolds
title Conformal Field Theories in Symplectic Manifolds
spellingShingle Conformal Field Theories in Symplectic Manifolds
Petronilo, Gustavo Xavier Antunes
Mecânica quântica
Função de Wigner
title_short Conformal Field Theories in Symplectic Manifolds
title_full Conformal Field Theories in Symplectic Manifolds
title_fullStr Conformal Field Theories in Symplectic Manifolds
title_full_unstemmed Conformal Field Theories in Symplectic Manifolds
title_sort Conformal Field Theories in Symplectic Manifolds
author Petronilo, Gustavo Xavier Antunes
author_facet Petronilo, Gustavo Xavier Antunes
author_role author
dc.contributor.none.fl_str_mv Santana, Ademir Eugênio de
Ulhoa, Sérgio Costa
dc.contributor.author.fl_str_mv Petronilo, Gustavo Xavier Antunes
dc.subject.por.fl_str_mv Mecânica quântica
Função de Wigner
topic Mecânica quântica
Função de Wigner
description Tese (doutorado em Física) — Universidade de Brasília, Brasília, 2024.
publishDate 2024
dc.date.none.fl_str_mv 2024-08-05T19:43:49Z
2024-08-05T19:43:49Z
2024-08-05
2024-03-07
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv PETRONITO, Gustavo Xavier Antunes. Conformal Field Theories in Symplectic Manifolds. 2024. 128 f. il. Tese (Doutorado em Física) — Universidade de Brasília, Brasília, 2024.
http://repositorio2.unb.br/jspui/handle/10482/49527
identifier_str_mv PETRONITO, Gustavo Xavier Antunes. Conformal Field Theories in Symplectic Manifolds. 2024. 128 f. il. Tese (Doutorado em Física) — Universidade de Brasília, Brasília, 2024.
url http://repositorio2.unb.br/jspui/handle/10482/49527
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da UnB
instname:Universidade de Brasília (UnB)
instacron:UNB
instname_str Universidade de Brasília (UnB)
instacron_str UNB
institution UNB
reponame_str Repositório Institucional da UnB
collection Repositório Institucional da UnB
repository.name.fl_str_mv Repositório Institucional da UnB - Universidade de Brasília (UnB)
repository.mail.fl_str_mv repositorio@unb.br
_version_ 1814508271949578240

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