Anti Self-Dual Yang-Mills, Modified Faddeev-Jackiw Formalism and Hidden BRS Invariance

TL;DR

This paper investigates the constraints and Hamiltonian structure of anti self-dual Yang-Mills equations using a modified Faddeev-Jackiw approach, revealing hidden BRS invariance and bi-Hamiltonian properties.

Contribution

It introduces a novel analysis of ASDYM constraints via the modified Faddeev-Jackiw method and uncovers hidden BRS invariance and bi-Hamiltonian structure in the system.

Findings

Constraints analyzed in K and J gauges

Hamiltonian flow established through hidden BRS invariance

ASDYM exhibits bi-Hamiltonian nature and compatible symplectic structures

Abstract

We analyze the constraints for a system of anti self-dual Yang-Mills (ASDYM) equations by means of the modified Faddeev-Jackiw method in K and J gauges \`{a} la Yang. We also establish the Hamiltonian flow for ASDYM system through the hidden BRS invariance in both the gauges. Finally, we remark on the bi-Hamiltonian nature of ASDYM and the compatibility of the symplectic structures therein.