Title:	Conformal Field Theories in Symplectic Manifolds
Authors:	Petronilo, Gustavo Xavier Antunes
Orientador(es)::	Santana, Ademir Eugênio de
Coorientador(es)::	Ulhoa, Sérgio Costa
Assunto::	Mecânica quântica Função de Wigner
Issue Date:	5-Aug-2024
Data de defesa::	7-Mar-2024
Citation:	PETRONITO, Gustavo Xavier Antunes. Conformal Field Theories in Symplectic Manifolds. 2024. 128 f. il. Tese (Doutorado em Física) — Universidade de Brasília, Brasília, 2024.
Abstract:	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.
metadata.dc.description.unidade:	Instituto de Física (IF)
Description:	Tese (doutorado em Física) — Universidade de Brasília, Brasília, 2024.
metadata.dc.description.ppg:	Programa de Pós-Graduação em Física
Appears in Collections:	Teses, dissertações e produtos pós-doutorado

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