Dualities between Poisson brackets and antibrackets

TL;DR

This paper explores the deep mathematical dualities between Poisson brackets and antibrackets, introducing generalized brackets and master equations, highlighting their symmetric relationships and extending the theoretical framework.

Contribution

It introduces generalized brackets involving higher antibrackets and Poisson brackets, along with generating functions and master equations, expanding the understanding of their dualities.

Findings

Expressed antibrackets in terms of Poisson brackets and vice versa

Introduced generalized brackets with higher structures

Provided symmetric formulations and master equations

Abstract

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer-Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.