Explicit construction of the classical BRST charge for nonlinear algebras

TL;DR

This paper presents an explicit formula and graphical representation for the BRST charge in Poisson superalgebras, solving the master equation by splitting it into two parts.

Contribution

It introduces a novel explicit construction of the BRST charge for nonlinear algebras, including a solution method and diagrammatic interpretation.

Findings

Derived an explicit formula for the BRST charge

Provided a graphical diagrammatic representation

Solved the master equation for Poisson superalgebras

Abstract

We give an explicit formula for the Becchi-Rouet-Stora-Tyutin (BRST) charge associated with Poisson superalgebras. To this end, we split the master equation for the BRST charge into a pair of equations such that one of them is equivalent to the original one. We find the general solution to this equation. The solution possesses a graphical representation in terms of diagrams.