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Gauge invariant actions for the noncommutative phase-space relativistic particle

Grupo de Física Teórica e Física Matemática, Universidade Federal Rural do Rio de Janeiro, 23890-971, Seropédica, RJ, Brazil

Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora, MG, Brazil

E-mail Address: evertonabreu@ufrrj.br

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and

Cresus F. L. Godinho

Grupo de Física Teórica e Física Matemática, Universidade Federal Rural do Rio de Janeiro, 23890-971, Seropédica, RJ, Brazil

E-mail Address: crgodinho@ufrrj.br

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https://doi.org/10.1142/S0217732317502157Cited by:1 (Source: Crossref)

Abstract

Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac’s point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act towards the constraints so that we have carried out the conversion of second to first-class constraints through the Batalin–Fradkin–Fradkina–Tyutin formalism, obtaining the second gauge invariant Lagrangian.

Keywords:

PACS: 11.10.Ef, 11.10.Nx, 11.15.Kc

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