Gauge conditions for an Abelian Chern-Simons system consistent with equations of motion

TL;DR

This paper performs a complete constraint analysis and identifies gauge conditions for an Abelian Chern-Simons system with a scalar field, ensuring consistency with equations of motion and relativistic invariance.

Contribution

It introduces gauge conditions compatible with equations of motion for the Abelian Chern-Simons system, ensuring relativistic invariance and anomaly-free gauge invariants.

Findings

Gauge conditions consistent with equations of motion are identified.

Relativistic invariance under boosts is achieved with these gauge choices.

Gauge invariant quantities are shown to be free of transformation anomalies.

Abstract

Complete constraint analysis and choice of gauge conditions consistent with equations of motion is done for Abelian Chern Simons field interacting minimally with a complex scalar field. The Dirac-Schwinger consistency condition is satisfied by the reduced phase space Hamiltonian density with respect to the the Dirac bracket. It is shown that relativistic invariance under boosts can be obtained only if gauge conditions were chosen consistent with the equations of motion. Moreover all gauge invariant quantities are shown to be free of transformation anomaly.