The Hamilton-Jacobi analysis for higher order Maxwell-Chern-Simons gauge theory

TL;DR

This paper applies the Hamilton-Jacobi formalism to analyze the symmetries of higher-order Maxwell-Chern-Simons gauge theory and compares it with the Gitman-Lyakhovich-Tyutin approach.

Contribution

It provides a comprehensive Hamilton-Jacobi analysis of the higher-order Maxwell-Chern-Simons theory and compares it with the GLT formalism, highlighting their consistencies.

Findings

Identified all symmetries of the higher-order Maxwell-Chern-Simons theory.

Derived the complete set of Hamilton-Jacobi Hamiltonians.

Compared and validated the results with the Gitman-Lyakhovich-Tyutin framework.

Abstract

By using the Hamilton-Jacobi [$HJ$] framework the higher-order Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential are reported, from which all symmetries of the theory are identified. In addition, we complete our study by performing the higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results of both formalisms.