BFV-BRST analysis of equivalence between noncommutative and ordinary gauge theories

TL;DR

This paper investigates the constrained Hamiltonian structure of noncommutative U(1) gauge theory, demonstrating its equivalence to ordinary gauge theory through BFV-BRST formalism and analyzing gauge fixing.

Contribution

It provides a BFV-BRST analysis showing the equivalence between noncommutative and ordinary gauge theories using a generalized phase space approach.

Findings

Constraints are first class but do not form an Abelian algebra.

BFV-BRST charge has a vanishing generalized Poisson bracket.

Equivalence is achieved via a solution in the generalized phase space.

Abstract

Constrained hamiltonian structure of noncommutative gauge theory for the gauge group U(1) is discussed. Constraints are shown to be first class, although, they do not give an Abelian algebra in terms of Poisson brackets. The related BFV-BRST charge gives a vanishing generalized Poisson bracket by itself due to the associativity of *-product. Equivalence of noncommutative and ordinary gauge theories is formulated in generalized phase space by using BFV-BRST charge and a solution is obtained. Gauge fixing is discussed.