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Master's Dissertation
DOI
https://doi.org/10.11606/D.43.2020.tde-27042020-170559
Document
Author
Full name
Xirliane Muniz Vasconcelos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Brandt, Fernando Tadeu Caldeira (President)
Dias, Alex Gomes
Nascimento, Jose Roberto Soares do
Title in Portuguese
Teorias de gauge no formalismo de primeira ordem com efeitos de temperatura finita
Keywords in Portuguese
Formalismo de Matsubara
Formalismo de Primeira Ordem
Teoria de gauge
Yang-Mills
Abstract in Portuguese
Este trabalho aborda as teorias de gauge nos formalismos de primeira ordem, em particular a teoria de Yang-Mills. É mostrado que os formalismos de primeira e segunda ordem da teoria de Yang-Mills são equivalentes ao nível clássico. Ambos os formalismos são quantizados e as regras de Feynman correspondentes são obtidas. Para verificar a equivalência ao nível quântico são calculados os diagramas de Feynman de 1-loop à temperatura zero e à temperatura finita, onde é usado o formalismo do tempo imaginário para estudar o comportamento à altas temperaturas. Neste regime é verificado a equivalência das auto-energias dos bósons de gauge, assim como o fato dos demais diagramas possuírem uma dependência subdominante na temperatura equivalente ao o mesmo tipo de divergência logarítmica dos diagramas à temperatura zero.
Title in English
First-order formalism gauge theories with finite temperature effects
Keywords in English
First order formalism
Gauge theory
Matsubara formalism
Yang-Mills
Abstract in English
This work deals with gauge theories in the first-order formalism, in particular, the Yang-Mills theory. It is shown that the first and second-order formalisms of the Yang-Mills theory are equivalent at the classic level. Both formalisms are quantized and the corresponding Feynman rules are obtained. To verify equivalence at the quantum level, one-loop Feynman diagrams are computed at both zero and finite temperature, where imaginary time formalism is used to study the high-temperature behaviour. In this regime, we verify the equivalence of the gauge bosons self-energies, as well as the fact that the other diagrams have a subdominant temperature dependence, which has the same type of logarithmic temperature dependence as the divergent part at zero temperature.
 
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Publishing Date
2020-05-12
 
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