BRST charges for finite nonlinear algebras

TL;DR

This paper extends the BRST construction to quadratic algebras with three generators, revealing a family of algebras with dual BRST charges forming a complex, thus broadening the algebraic framework for quantum constraints.

Contribution

It constructs the BRST charge for a class of quadratic algebras with three generators and explores their dual BRST charges forming a double complex.

Findings

BRST charge for quantum Lie algebra with three generators is constructed.

A one-parametric family of quadratic algebras admits a redefined, conventional BRST charge.

Each algebra in the family has two independent, anticommuting BRST charges forming a double complex.

Abstract

Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a non-linear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.