Abstract:Resumo Revisamos a construção da teoria de gauge para os grupos de Lie semi-simples realizada por Utiyama em seu trabalho “Interpretação da Interação por Invariância Teórica”[1]. Mostramos que para manter a invariância de um sistema de campos ϕ A ( x ) sob um grupo de transformações a n parâmetros ϵ a ( x ) dependentes do ponto x μ é necessário introduzir um novo campo A μ a ( x ). Este campo auxiliar interage com ϕ como manifesto pela derivada covariante ∇ μ ϕ A. Determinamos a lei de tr… Show more
“…Besides the ordinary four-potential m A x ( ), a scalar field B x ( ) is introduced. Our proposal keeps the minimal coupling prescription suggested in the seminal works by Weyl [58,59], introduced more generally by Yang and Mills [3,4], and formalized by Utiyama [6]-see also [16]. This means that the gauge potential A μ appears in the definition of the (gauge) covariant derivative ∇ μ ∼ ∂ μ + A μ whereas the scalar field B does not.…”
Section: Introductionmentioning
confidence: 90%
“…However, Yang-Mills' proposal would not predict a massive m A a , which meant that SU(2) symmetry could not alone account for the weak-field interaction. Actually, the massless character of m A a within gauge theory was proved rigorously by Utiyama [6,16]. He showed that any term of the type…”
Utiyama's method is a deductive approach of building gauge theories for semi-simple groups of local transformations, including the Abelian U(1) case, the non-Abelian SU(N) group, and the gravitational interaction. Gauge theories à la Utiyama typically predict a massless gauge potential. This work brings a mass generation mechanism and Utiyama's method together thus giving mass to the interaction boson without breaking the gauge symmetry. Herein we devote our attention to the Abelian case. Two gauge potentials are introduced: a vetor field A_{\mu} and a scalar field B. The associated gauge-invariant field strengths F_{\mu\nu} and G_{\mu} are built from Utiyama's technique. Gauge invariance requirement upon the total Lagrangian (including matter fields and gauge fields) yields the conserved currents. Finally, we study the simplest type of Lagrangian involving the field strengths and obtain the related field equation. By imposing appropriate constraints on this particular example, Stueckelberg model is recovered.
“…Besides the ordinary four-potential m A x ( ), a scalar field B x ( ) is introduced. Our proposal keeps the minimal coupling prescription suggested in the seminal works by Weyl [58,59], introduced more generally by Yang and Mills [3,4], and formalized by Utiyama [6]-see also [16]. This means that the gauge potential A μ appears in the definition of the (gauge) covariant derivative ∇ μ ∼ ∂ μ + A μ whereas the scalar field B does not.…”
Section: Introductionmentioning
confidence: 90%
“…However, Yang-Mills' proposal would not predict a massive m A a , which meant that SU(2) symmetry could not alone account for the weak-field interaction. Actually, the massless character of m A a within gauge theory was proved rigorously by Utiyama [6,16]. He showed that any term of the type…”
Utiyama's method is a deductive approach of building gauge theories for semi-simple groups of local transformations, including the Abelian U(1) case, the non-Abelian SU(N) group, and the gravitational interaction. Gauge theories à la Utiyama typically predict a massless gauge potential. This work brings a mass generation mechanism and Utiyama's method together thus giving mass to the interaction boson without breaking the gauge symmetry. Herein we devote our attention to the Abelian case. Two gauge potentials are introduced: a vetor field A_{\mu} and a scalar field B. The associated gauge-invariant field strengths F_{\mu\nu} and G_{\mu} are built from Utiyama's technique. Gauge invariance requirement upon the total Lagrangian (including matter fields and gauge fields) yields the conserved currents. Finally, we study the simplest type of Lagrangian involving the field strengths and obtain the related field equation. By imposing appropriate constraints on this particular example, Stueckelberg model is recovered.
“…Porém, como era bem sabido por Pauli [8], as partículas intermediadoras dessa interação associada a simetria de isospin local são não massivas, contradizendo o fato da interação forte ser descrita por uma interação de curto alcance e partículas massivas. Paralelamente ao trabalho de Yang-Mills, Utiyama estabelece um cojunto de diretrizes para construir uma teoria de gauge para todos os grupos de Lie semi-simples e inclui também no estudo, a relação entre a gravitação na formulação de tetradas e o eletromagnetismo via conexão [9,10]. Nos dias atuais, o caráter geométrico das interações fundamentais ainda é explorado [11,12].…”
Resumo Este trabalho tem como objetivo introduzir e discutir a metodologia de Shaw-Deser para descrever a interação entre matéria e radiação via simetria de calibre (abeliana/não abeliana). Nas entrelinhas, a mensagem que pretendemos passar é como a “impressão digital” da simetria de calibre local está contida na simetria de calibre global, por meio de uma interação corrente-campo (Dirac/Schwinger) e uma análise mais algébrica (iterativa), complementando a abordagem geométrica de Yang-Mills/Utiyama.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.