A quantum BRST anti-BRST approach to classical integrable systems

TL;DR

This paper reformulates classical integrability conditions using quantum BRST anti-BRST methods, revealing natural emergence of Lax pairs and inverse scattering wavefunctions within a quantum framework.

Contribution

It introduces a novel quantum BRST anti-BRST formulation of classical integrable systems, connecting geometric Lax equations with quantum theory structures.

Findings

Lax pairs appear naturally in the quantum BRST anti-BRST framework

Inverse scattering wavefunctions emerge in specific sectors of the quantum theory

Liouville integrability conditions are reformulated in this quantum language

Abstract

We reformulate the conditions of Liouville integrability in the language of Gozzi et al.'s quantum BRST anti-BRST description of classical mechanics. The Das-Okubo geometrical Lax equation is particularly suited to this approach. We find that the Lax pair and inverse scattering wavefunction appear naturally in certain sectors of the quantum theory.