skip to main content
Idioma:
Primo Search
Clear Search Box
Search in: Busca Geral
Busca Avançada
Busca por Índices

Hidden symmetries in gauge theories & quasi-integrablility

Martins, Gabriel Luchini

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Física de São Carlos 2013-02-25

Acesso online

  • Título:
    Hidden symmetries in gauge theories & quasi-integrablility
  • Autor: Martins, Gabriel Luchini
  • Orientador: Ferreira, Luiz Agostinho
  • Assuntos: Cargas Conservadas; Espaço De Laços; Formulação De Curvature Nula; Simetrias Escondidas; Solitons
  • Descrição: This thesis is about some extensions of the ideas and techniques used in integrable field theories to deal with non-integrable theories. It is presented in two parts. The first part deals with gauge theories in 3 and 4 dimensional space-time; we propose what we call the integral formulation of them, which at the end give us a natural way of defining the conserved charges that are gauge invariant and do not depend on the parametrisation of space-time. The definition of gauge invariant conserved charges in non-Abelian gauge theories is an open issue in physics and we think our solution might be a first step into its full understanding. The integral formulation shows a deeper connection between different gauge theories: they share the same basic structure when written in the loop space. Moreover, in our construction the arguments leading to the conservation of the charges are dynamical and independent of the particular solution. In the second part we discuss the recently introduced concept called quasi-integrability: one observes soliton-like configurations evolving through non-integrable equations having properties similar to those expected for integrable theories. We study the case of a model which is a deformation of the non-linear Schr¨odinger equation consisting of a more general potential, connected in a way with the integrable one. The idea is to develop a mathematical approach to treat more realistic theories, which is in particular very important from the point of view of applications; the NLS model appears in many branches of physics, specially in optical fibres and Bose-Einstein condensation. The problem was treated analytically and numerically, and the results are interesting. Indeed, due to the fact that the model is not integrable one does not find an infinite number of conserved charges but, instead, a set of infinitely many charges that are asymptotically conserved, i.e., when two solitons undergo a scattering process the charges they carry before the collision change, but after the collision their values are recovered.
  • DOI: 10.11606/T.76.2013.tde-30042013-143928
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Física de São Carlos
  • Data de criação/publicação: 2013-02-25
  • Formato: Adobe PDF
  • Idioma: Inglês
Links
Voltar para lista de resultados
Ir para página anteriorAnterior Resultado  8 AvançarIr para próxima página

  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

Buscando em bases de dados remotas. Favor aguardar.