On a different BRST constructions for a given Lie algebra

TL;DR

This paper explores alternative BRST quantization methods for Lie algebra constraints, especially when some Cartan generators are unconstraining, leading to nonlinear ghost terms in the BRST charge.

Contribution

It introduces a new approach to BRST construction that handles systems with mixed first and second class constraints and nonlinear ghost structures.

Findings

Constructed BRST charges with nonlinear ghost terms

Addressed systems with unconstraining Cartan generators

Extended BRST methods for mixed constraint systems

Abstract

The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second class constraints. After the introduction auxiliary bosonic degrees of freedom for these cases, the corresponding BRST charges with the nontrivial structure of nonlinear terms in ghosts are constructed.