Teorias de gauge a la Utiyama

• Autor(a) principal: Acevedo, O.a.
• Data de Publicação: 2018
• Outros Autores: Cuzinatto, R.r., Pimentel, B.m., Pompeia, P.j.
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1590/1806-9126-rbef-2018-0007; http://hdl.handle.net/11449/158171
• topic: gauge theories; Utiyama method; teorias de gauge; método de Utiyama

Abstract We review the construction of the gauge theory for semi-simple Lie groups by Utiyama in “Invariant Theoretical Interpretation of Interaction”[1]. It is shown an auxiliary fieldA μ ax must be introduced in order to keep the system of fieldϕ Ax invariant under a transformation group depending onn parameterϵ ax. This auxiliary field interacts withϕ through the covariant derivative∇ μϕ A. We determine the transformation law for A μ a under the x μ-dependent Lie group and calculate the field strengthF μ ν ax. Moreover, we specify the conserved current Ja μ related to the invariance of the complete system. The paper ends with the application of the general theory to the cases of the charged particle in an electromagnetic field and of the Yang-Mills potential under isotopic spin space transformations; we briefly address the matter of the gravitational field as a gauge theory; finally, we comment on the extension of Utiyama's theory forL A =L A A μ a ;∂ νA μ a ;∂ ρ∂ νA μ ax.