Embedding Commutative and Noncommutative Theories in the Symplectic Framework

TL;DR

This paper explores a symplectic formalism approach to gauge embedding of both commutative and noncommutative theories, providing a more controlled and direct method for constructing gauge-invariant models.

Contribution

It introduces a novel symplectic framework for gauge embedding that simplifies the choice of gauge generators and addresses the arbitrariness problem in the process.

Findings

Successfully embedded the Proca model, fluid model, and noncommutative self-dual model.

Demonstrated easier and more direct selection of gauge generators.

Provided insights into controlling the final Lagrangian and resolving arbitrariness.

Abstract

This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative self-dual model. In the process of this new path of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and puts some light on the so called ''arbitrariness problem".