Hamiltonian embedding of the massive noncommutative U(1) theory

TL;DR

This paper demonstrates how to embed the massive noncommutative U(1) gauge theory into a gauge theory framework using the BFFT Hamiltonian formalism, addressing unique algebraic challenges posed by noncommutativity.

Contribution

It introduces a method to embed the massive noncommutative U(1) theory into a gauge theory using BFFT formalism, overcoming non-Abelian algebraic complexities.

Findings

Successful embedding of the noncommutative U(1) into a gauge theory.

Development of an involutive Hamiltonian for the embedded theory.

Handling of infinite iterative steps due to non-Abelian algebraic structure.

Abstract

We show that the massive noncommutative U(1) can be embedded in a gauge theory by using the BFFT Hamiltonian formalism. By virtue of the peculiar non-Abelian algebraic structure of the noncommutative massive U(1) theory, several specific identities involving Moyal commutators had to be used in order to make the embedding possible. This leads to an infinite number of steps in the iterative process of obtaining first-class constraints. We also shown that the involutive Hamiltonian can be constructed.