Antibracket as the Hamiltonian Structure of a classical integrable system

TL;DR

This paper demonstrates that the time evolution in a supersymmetric extension of the KP hierarchy is Hamiltonian, with the canonical bracket being an antibracket, offering new insights into supersymmetric Hamiltonian systems.

Contribution

It introduces the antibracket as the Hamiltonian structure for a supersymmetric integrable system, linking classical integrability with gauge theory quantization concepts.

Findings

Time evolution is shown to be Hamiltonian in the supersymmetric KP hierarchy.

The canonical bracket is identified as an antibracket, analogous to gauge theory quantization.

Provides a new perspective on supersymmetric Hamiltonian systems.

Abstract

The time evolution in a supersymmetric extension of the Kodomtsev-Petviashvilli hierarchy, a classical integrable system, is shown to be Hamiltonian. The canonical bracket associated to the Hamiltonian evolution is the classical analog of the antibracket encountered in the quantization of gauge theories. This provides a new understanding of supersymmetric Hamiltonian systems.