An improved Gauge Unfixing formalism and the Abelian Pure Chern Simons Theory

TL;DR

This paper introduces an improved Gauge Unfixing formalism that directly modifies phase space variables to produce gauge-invariant quantities, successfully applied to Abelian Pure Chern Simons Theory, preserving gauge symmetry.

Contribution

It presents a novel variant of the Gauge Unfixing formalism that directly alters phase space variables, maintaining gauge invariance in Abelian Chern Simons Theory.

Findings

Successfully derived gauge-invariant Hamiltonian and Lagrangian

Preserved gauge symmetry in the Abelian Pure Chern Simons Theory

Demonstrated advantages of the new formalism over traditional methods

Abstract

We propose a variant scheme of the Gauge Unfixing formalism which modifies directly the original phase space variables of a constrained system. These new variables are gauge invariant quantities. We apply our procedure in a mixed constrained system that is the Abelian Pure Chern Simons Theory where several gains are obtained. In particular, from the gauge invariant Hamiltonian and using the inverse Legendre transformation, we obtain the same initial Abelian Pure Chern Simons Lagrangian as the gauge invariant Lagrangian. This result shows that the gauge symmetry of the action is certainly preserved.