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Doctoral Thesis
DOI
10.11606/T.43.1998.tde-27022014-132628
Document
Author
Full name
Paulo Barbosa Barros
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1998
Supervisor
Committee
Guitman, Dmitri Maximovitch (President)
Frenkel, Josif
Helayël- Neto, José Abdalla
Wreszinski, Walter Felipe
Zimerman, Abraham Hirsz
Title in Portuguese
Algumas Aplicações de Integrais de Trajetória Grassmannianas na Teoria Quântica Moderna
Keywords in Portuguese
Álgebra de berezin
Álgebra de grassmann
Cálculo de operadores
Fator espinoral
Integrais de trajetória
Abstract in Portuguese
Este trabalho é dedicado à aplicação de integrais de trajetória de Grassmann para o cálculo de operadores relevantes aos problemas da teoria quântica relativística. Primeiramente uma visão geral detalhada do método é fornecida. Então concentramos nas definições e aplicações das integrais de trajetória sobre as variáveis de Grassmann. Discutimos, em detalhe, um importante papel das integrais de trajetória de Grassmann na representação de propagadores de partículas relativísticas. Derivamos o chamado fatores de spin para tais representações, fazendo as integrações Grasmannianas. Uma contribuição completamente original foi feita aplicando tais integrais ao cálculo de operadores. Derivamos, desta forma, um conjunto de fórmulas novas para as funções de operadores das matrizes y. A aplicações de tais fórmulas são apresentadas.
Title in English
Some Applications of Grassmannianas Trajectory Integrals in Modern Quantum Theory
Keywords in English
Berezin algebra
Calculation operators
Espinoral factor
Grassmann algebra
Trajectory integrals
Abstract in English
This work is devoted to an application of Grassmann path integrals to operator calculus relevant to problems of relativistic quantum theory. A detailed survey of path integral method is given first. Then we concentrate ourselves on definitions and applications of path integrals over Grassmann variables. We discuss in detail an important role of Grassmann path integrals in representations of relativistic particle propagators. We derive the so called spin factors for such representations doing Grassmann integrations. A completely original contribution was made in application of such integrals to operator calculus. We have derived in such a way a set of new formulas for operator functions of y-matrices. Applications of such formulas are presented.
 
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RE45363Barros.pdf (47.74 Mbytes)
Publishing Date
2014-02-28
 
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