Banca de DEFESA: Gustavo Xavier Antunes Petronilo

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Gustavo Xavier Antunes Petronilo
DATE: 07/03/2024
TIME: 14:00
LOCAL: IF
TITLE:

Conformal Field Theories in Symplectic Manifolds

KEY WORDS:

Conformal field theory, Galilean Covariance, Carrollian Covariance, Symplectic quantum mechanics, Wigner Function

PAGES: 105
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

This work investigates the notion of a conformal group and derives a representation for symplectic quantum mechanics, in the manifold G in a consistent manner, using the Wigner function method. We study two non-Lorentzian conformal symmetries: the Conformal Carrollian group and the Schrödinger 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 Schrödinger (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-Schrödinger problem in phase-space. We investigate the non-relativistic part of the StefanBoltzmann law and the Casimir effect for the spin 0 and spin 1/2 particles with thermofield dynamics, also within the framework of Galilean covariance.

COMMITTEE MEMBERS:
Presidente - ***.309.881-** - ADEMIR EUGENIO DE SANTANA - UnB
Externo à Instituição - HARA DESSANO MENEZES - IFB
Externo à Instituição - HUMBERTO BELICH JUNIOR - UFES
Externo ao Programa - 1803399 - RONNI GERALDO GOMES DE AMORIM - UnBInterno - 404867 - TARCISIO MARCIANO DA ROCHA FILHO