New Gauge Invariant Formulation of the Chern-Simons Gauge Theory

TL;DR

This paper introduces a new gauge invariant approach to formulating the relativistic scalar field interacting with Chern-Simons gauge fields, resolving issues with gauge invariance of Poincaré generators.

Contribution

It presents a novel gauge invariant formulation that aligns with gauge fixed methods and constructs improved, gauge invariant Poincaré generators from the symmetric energy-momentum tensor.

Findings

Canonical Poincaré generators are not gauge invariant.

Improved generators are gauge invariant and satisfy Poincaré algebra.

Formulation is consistent with gauge fixed approaches.

Abstract

A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore we find that canonical (Noether) Poincar\'e generators are not gauge invariant even on the constraints surface and do not satisfy the (classical) Poincar\'e algebra. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the classical Poincar\'e algebra.