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CANONICAL STRUCTURE OF GAUGE INVARIANCE PROCA'S ELECTRODYNAMICS THEORY
ESTRUCTURA CANÓNICA DE LA TEORÍA ELECTRODINÁMICA DE LA INVARIANZA GAUGE DE PROCA
Keywords:
Dirac's method, Faddeev-Jackiw's formalism, Constraint analysis, Dirac brackets, Generalized brackets (en)Método de Dirac, Formalismo de Faddeev-Jackiw, Análisis de vínculos, Corchetes de Dirac, Corchetes Generalizados (es)
Proca's electrodynamics describes a theory of massive photons which is not gauge invariant. In this paper we show that the gauge invariance is recovered if a scalar field is properly incorporated into the theory. We followed the Dirac's technique to perform a detailed analysis of the constraint structure of the theory. Appropriate gauge conditions were derived to eliminate the first class constraints and obtain the Dirac's brackets of the independent dynamical variables. Alternatively, the generalized symplectic formalism method is used to study the gauge invariance Proca's electrodynamics theory. After fixing the gauge, the generalized brackets are calculated and the equivalence with the Dirac's brackets is shown.
La electrodinámica de Proca describe una teoría de fotones masivos que no es invariante de gauge. En este trabajo se mostrará que la libertad de gauge es restaurada si un campo escalar es apropiadamente incorporado en la teoría. El método de Dirac es utilizado para realizar un detallado análisis de la estructura de vínculos de la misma. Apropiadas condiciones de gauge fueron derivadas con el fin de eliminar los vínculos de primera clase y obtener los corchetes de Dirac entre las variables dinámicas independientes. De manera alternativa, la formulación simplectica generalizada es utilizada para estudiar la teoría electromagnética de Proca invariante de gauge. Después de fijar el gauge, los corchetes generalizados son calculados y la equivalencia con los corchetes de Dirac es mostrada.
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