https://repositorio.ufba.br/handle/ri/41510 2026-05-03T19:07:39Z 2026-05-03T19:07:39Z Santos, Matheus Ferreira dos https://repositorio.ufba.br/handle/ri/41817 2025-04-16T11:11:13Z 0002-02-04T00:00:00Z

Título: Introdução à pseudomecânica: formalismo e aplicações na descrição clássica de partículas com Spin 1/2. Autor(es): Santos, Matheus Ferreira dos Primeiro Orientador: Flores, Carlos Enrique Valcarcel Abstract: In this work, we use anticommutative variables from Grassmann algebra to generalize the Lagrangian and Hamiltonian formalisms, aiming to describe massive particles with spin 1/2, both relativistic and non-relativistic, within a framework called pseudomechanics. Initially, we present the fundamental concepts of Grassmann algebra, emphasizing the anticommutative property of its elements. The incorporation of these variables into the aforementioned formalisms resulted in new Euler-Lagrange and Hamilton equations, as well as extensions of Noether's theorem and Poisson brackets. Given that pseudomechanical systems are intrinsically singular, we introduced Dirac's formalism to properly handle such systems. In the non-relativistic regime, we developed models describing particles interacting with external magnetic fields, spin-orbit coupling, and interactions between the spins of two particles, further demonstrating the conservation of total angular momentum in systems with rotational symmetry. In the relativistic regime, we verified the invariance of the system under supersymmetry and showed that the canonical quantization of this formalism leads to the Dirac equation, linking it to the symmetries associated with supersymmetric transformations. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Trabalho de Conclusão de Curso

0002-02-04T00:00:00Z Souza, Pedro Moreira Machado de https://repositorio.ufba.br/handle/ri/41546 2025-03-24T11:37:13Z 2024-02-23T00:00:00Z

Título: Uma introdução à gravitação em 3D como uma teoria de Gauge: soluções e simetrias. Autor(es): Souza, Pedro Moreira Machado de Primeiro Orientador: Valcarcel Flores, Carlos Enrique Abstract: Lower dimensional gravity provides a toy model capable of helping in the understanding of open questions in physics, such as quantum gravity. Three dimensional gravity is equivalent to the Chern-Simons (gauge) theory, seeming when explicitly written in the first order formalism. The goal of this project is to investigate gravity in three dimensions under a gauge theory aspect, focusing on the solutions and symmetries of the model. Thus, it is intended to study the first-order action equivalent to Einstein-Hilbert action expressed in terms of the Dreibein and the spin connection, explore the constraint structure of the Chern-Simons theory via Dirac procedure, and, in the particular case of Anti-de Sitter space, obtain the BTZ black hole solution and the asymptotic symmetries. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Trabalho de Conclusão de Curso

2024-02-23T00:00:00Z