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Master's Dissertation
DOI
Document
Author
Full name
Rogerio Tadeu da Rocha Camargo Filho
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Brandt, Fernando Tadeu Caldeira (President)
Ferrari, Alysson Fabio
Natale, Adriano Antonio
Title in Portuguese
Teorias de calibre no formalismo de 1ª ordem
Keywords in Portuguese
Computação Simbólica
Formalismo de 1a Ordem
Regularização dimensional
Teorias de Calibre
Yang-Mills
Abstract in Portuguese
O principal objetivo do presente trabalho é expor o procedimento de quantização de teorias de Yang-Mills, através do método de Faddeev-Popov, no formalismo de 1a Ordem, e investigar num primeiro momento sua equivalência (clássica e quântica) ao formalismo usual (2a Ordem) e algumas de suas aplicações, principalmente no cálculo de correções quânticas. Para isso, ideias gerais a respeito do processo de quantização via formalismo de Faddeev-Popov foram expostas, e posteriormente utilizadas no processo de quantização de teorias de Yang-Mills no formalismo de 1a Ordem. Apresenta-se também as ideias gerais relativas ao método de regularização dimensional utilizado no cálculo de correções quânticas à nível de 1-loop para a teoria de Yang-Mills no formalismo de 1a ordem, utilizando-se, para isso, computação simbólica. Foi demonstrado que via formalismo de 1a Ordem, a estrutura ultravioleta encontrada no propagador do bóson de gauge é consistente com a renormalizabilidade da teoria. Embora tenhamos diferenças quanto a estrutura das interações neste novo formalismo, a estrutura das divergências ultravioletas continua a mesma do formalismo usual.
Title in English
First Order Formalism in gauge Theories
Keywords in English
Di- mensional Regularization
First order formalism
Gauge Theories
Symbolic Computation
Yang-Mills
Abstract in English
The main objective of the present work is to expose the quantization procedure of Yang- Mills theories in first order formalism, by Faddeev Popov's method. We want to investigate the classical and quantum equivalence between first and second order formalism, and look and analyze the differences in practical calculations of quantum corrections. Therefore, the general ideas about quantizantion by Faddeev-Popov's method was exposed, and used later in first order theory. It is also presented in this work, the main ideas concerning to dimensional regularization used in quantum corrections calculations at one-loop order for Yang-Mills theories, using for that, symbolic computation. It has been shown that upon using the first order formalism, the ultraviolet structre found in gauge boson propagator is also consistent to the theory's renormalizability. Although we have differences concerning to interactions structures in this new formalism, the ultraviolet structures from usual formalism is also found in it.
 
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Publishing Date
2019-05-29
 
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