Classical BRST charge for nonlinear algebras

TL;DR

This paper develops a method to construct the classical nilpotent BRST charge for nonlinear gauge algebras characterized by polynomial constraints, providing explicit formulas especially for quadratic cases.

Contribution

It derives conditions for the BRST charge to have a simple form in nonlinear algebras and explicitly computes the third order ghost contribution for quadratic algebras.

Findings

Restrictions on structure constraints for simple BRST form

Explicit third order ghost term for quadratic algebras

Framework applicable to polynomial gauge algebras

Abstract

We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints. Such a polynomial is characterized by the coefficients forming a set of higher order structure constraints. Assuming the set of constraints to be linearly independent, we find the restrictions on the structure constraints when the nilpotent BRST charge can be written in a simple and universal form. In the case of quadratically nonlinear algebras we find the expression for third order contribution in the ghost fields to the BRST charge without the use of any additional restrictions on the structure constants.