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Doctoral Thesis
DOI
10.11606/T.43.1978.tde-02122013-141331
Document
Author
Full name
Miguel El Afioni
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1978
Supervisor
Committee
Fleming, Henrique
Koberle, Roland
Swieka, Jorge André
Ventura, Ivan
Title in Portuguese
Estudo perturbativo de um modelo bi-dimensional com acoplamento corrente axial : gradiente de um campo pseudo-escalar.
Keywords in Portuguese
Teoria quântica de campo
Abstract in Portuguese
Nesta tese, um estudo é feito do modelo bi-dimensional descrito pela densidade de Lagrangeana. Na primeira parte deste trabalho, discute- se a teoria de perturbação na constante de acoplamento g para as funções de Green. Mostra-se como e possível construir um esquema de renormalização de modo que não sejam induzidas interações quadri-lineares nos férmions quando M=0. Aplicando a identidade de Ward da corrente axial, prova-se então, que o limite M = 0 coincide, em qualquer ordem de g, com as funções de Green do modelo com massa do fermion nula, que e exatamente solúvel. Na segunda parte da tese , o termo de massa do férmion em L é tratado como uma perturbação em torno da teoria não livre. Após uma resomação parcial da série perturbativa, mostra-se que as funções de Green Euclidianas tornam-se finitas no intervalo O g POT. 2< pela introdução de um contra-termo proporcional a (:cos2g:1). A quebra da invariança pelas transformações - POT. 5 é verificada explicitamente por meio da identidade de Ward da corrente axial.
Title in English
Perturbative study of a two-dimensional model describing a coupled of axial current to a pseudo-scalar field.
Keywords in English
Quantum field theory
Abstract in English
In this thesis, a study is made of the two-dimensional model described by the Lagrangean density. In the first part of this work, the perturbation theory in the coupling constant g is discussed for the Green functions. It is shown how to construct a renormalization scheme such that no four-linear interactions in the fermion field are induceded when m=0 by applying the axial current Ward identity, it is then proved that the M=O limit agrees, in every order of g, with the Green functions of the soluble model with massless fermion. In the second part of the thesis, the fermion mass term in L is considered as a perturbation on the interacting theory. After a partial resummation of the perturbative series, it is shown that the Euclidean Green functions are made finite for 0g²< introducing a counter-term proportional to (:cos2g:1). Breaking of -5 symmetry is explicity verified through the axial current Ward identity.
 
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RE30958Afioni.pdf (4.02 Mbytes)
Publishing Date
2014-02-18
 
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