Hamiltonian symplectic embedding of the massive noncommutative U(1) Theory

TL;DR

This paper introduces a symplectic embedding method for the massive noncommutative U(1) theory, providing a systematic approach to embed it into a gauge theory with dynamically equivalent Hamiltonian densities.

Contribution

It presents an alternative symplectic framework for embedding the massive noncommutative U(1) theory, differing from the BFFT formalism, and achieves the embedded Hamiltonian after finite steps.

Findings

Successfully embedded the theory using symplectic formalism

Provided a finite-step iterative process for embedding

Demonstrated equivalence of embedded Hamiltonian densities

Abstract

We show that the massive noncommutative U(1) theory is embedded in a gauge theory using an alternative systematic way, which is based on the symplectic framework. The embedded Hamiltonian density is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. This alternative formalism of embedding shows how to get a set of dynamically equivalent embedded Hamiltonian densities.