O campo escalar no formalismo de Duffin-Kemmer-Petiau
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Data
2001-11
Autores
Lunardi, José Tadeu Teles [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho consideramos alguns aspectos da teoria de campo escalar em interação no formalismo de Duffin-Kemmer-Petiau (DKP). No nível clássico estudamos dois casos: a interação mínima eletromagnética e a interação gravitacional no contexto das teorias de Einstein-Cartan e Teleparalelismo. No primeiro caso, mostramos que o formalismo DKP é completamente equivalente ao formalismo de Klein-Gordon (KG). No segundo caso, mostramos que a presença de torção no contexto da teoria de Einstein-Cartan destrói essa equivalência. Enquanto no formalismo KG não há interação entre campo escalar e a torção, no formalismo DKP essa interação surge de maneira natural. Discutimos a diferença entre a interação com a torção nos contextos das teorias de Einstein-Cartan e do Teleparalelismo. No nível quântico formulamos a eletrodinâmica escalar via formalismo DKP no contexto da teoria de perturbação causal de Bogoliubov-Epstein-Glaser, de maneira a definir a matriz S de espalhamento de uma forma não efetiva e matematicamente rigorosa, livre de divergências. Consideramos, em ordem mais baixa de teoria de perturbação, o espalhamento Compton, a polarização do vácuo, a auto-energia da partícula escalar e a correção de vértice no limite de momento transferido nulo. Todos os resultados obtidos nesses cálculos concordam com aqueles obtidos na teoria DKP efetiva usual e nos tratamentos via formalismo de Klein-Gordon, corroborando assim a equivalência entre ambos os formalismos nesse contexto
Abstracts: In this work we consider some aspects of the interacting scalar field in the Diffin-Kemmer-Patiau (DKP) formalism. At the classical level we study two cases: the minimal electromagnetic interaction and the gravitational interaction in the context of Einstein-Cartan and Teleparalelismo theories. In the former case we show that DKP formalism is completely equivalent to the Klein-Gordon (KG) one. In the later case we show that a nonvanishing torsion in einstein-Cartan theory breaks this equivalence. While in the KG formalism the scalar field does not interact with torsion, in DKP formalism this interaction naturally arises. We discuss the difference between this interaction with torsion in the context of Einstein-Cartan and Teleparalelism. At the quantum level we formulate scalar electrodynamics via DKP formalism in the framework of Bogoliubov-Epstein-Glaser causal perturbation theory. We define the S-matrix in a non effective and mathematically rigorous way. We consider, in the lowest order of perturbation theory, the Compton scattering, vacuum polarization, scalar self-energy and the vertex function at the limit of zero transferred momentum. In these computations all our results agree with those obtained first in the usual effective theory and in the Klein-Gordon based approaches, which corroborate the statement about the equivalence of both formalism in this context
Abstracts: In this work we consider some aspects of the interacting scalar field in the Diffin-Kemmer-Patiau (DKP) formalism. At the classical level we study two cases: the minimal electromagnetic interaction and the gravitational interaction in the context of Einstein-Cartan and Teleparalelismo theories. In the former case we show that DKP formalism is completely equivalent to the Klein-Gordon (KG) one. In the later case we show that a nonvanishing torsion in einstein-Cartan theory breaks this equivalence. While in the KG formalism the scalar field does not interact with torsion, in DKP formalism this interaction naturally arises. We discuss the difference between this interaction with torsion in the context of Einstein-Cartan and Teleparalelism. At the quantum level we formulate scalar electrodynamics via DKP formalism in the framework of Bogoliubov-Epstein-Glaser causal perturbation theory. We define the S-matrix in a non effective and mathematically rigorous way. We consider, in the lowest order of perturbation theory, the Compton scattering, vacuum polarization, scalar self-energy and the vertex function at the limit of zero transferred momentum. In these computations all our results agree with those obtained first in the usual effective theory and in the Klein-Gordon based approaches, which corroborate the statement about the equivalence of both formalism in this context
Descrição
Palavras-chave
Teoria de campos escalares
Como citar
LUNARDI, José Tadeu Teles. O campo escalar no formalismo de Duffin-Kemmer-Petiau. 2001. 93 f. Tese (doutorado) - Universidade Estadual Paulista, Instituto de Física Teórica, 2001.