• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
10.11606/D.43.2013.tde-24092014-134946
Document
Author
Full name
Nelson Javier Buitrago Aza
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Teotonio Sobrinho, Paulo (President)
Lyra, Jorge Lacerda de
Mendes, Tereza Cristina da Rocha
Title in Portuguese
Limites topológicos do modelo Gauge-Higgs com simetria Z(2) em uma rede bidimensional
Keywords in Portuguese
Álgebras de Hopf
Grupos abelianos.
Limites topológicos
Modelo de Gauge-Higgs
Teoria de Gauge na rede
Abstract in Portuguese
Nesta dissertação estudamos as teorias de gauge acoplada com campos de matéria em variedades bidimensionais. Para isso, descrevemos primeiro um formalismo em duas e três dimensões o qual é baseado na ideia de Kuperberg de definir um invariante topológico em três dimensões usando álgebras de Hopf e diagramas de Heegaard. O uso do formalismo é útil para este trabalho pois é fácil a identificação de limites topológicos sem resolver o modelo. Também escrevemos o modelo de gauge com campos de matéria usando uma fixação de gauge chamada de gauge unitário. Trabalhamos com o grupo abeliano $\mathbb_$ e explicamos com detalhe o caso $\mathbb_$. Calculamos as funções de partição e loops de Wilson para este grupo nos diferentes limites topológicos. Mostramos que existem casos nos quais os resultados dependem da triangulação mas de maneira trivial, estes casos foram chamados de quase-topológicos.
Title in English
Topological Limits in the Gauge-Higgs Model with Z(2) Symmetry in a Bidimensional Lattice
Keywords in English
Abelian Groups
Gauge-Higgs Model
Hopf Algebras
Lattice Gauge Theory
Topological Limits
Abstract in English
In this thesis we study gauge theories coupled with matter fields in two-dimensional manifolds. In order to proceed we first describe a formalism in two and three dimensions which is based on the idea of Kuperberg of defining a topological invariant in three dimensions using Hopf algebras and Heegaard diagrams. The use of this formalism is useful here because it is easy to identify topological limits without solving the model. Furthermore, we write the gauge model with matter fields choosing the unitary gauge. We work with abelians groups Z(n) and explain the Z(2) case in detail. We calculate partition functions and Wilson loops for this group in the different topological limits. We show that, there were cases in which the results depended on the triangulation but in a trivial way, these cases are called quasi-topological.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
DiserJavier.pdf (3.76 Mbytes)
Publishing Date
2014-10-10
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.