Computing the BRST Operator Used in Quantization of Gauge Theories

TL;DR

This paper presents an algorithmic approach and computer algebra tools for computing the BRST charge in a broad class of non-holonomic quantum systems, facilitating complex calculations for nonlinear algebras.

Contribution

It introduces two REDUCE programs that automate the computation of the BRST charge for nonlinear algebras in quantum gauge theories, a novel advancement.

Findings

Algorithms successfully compute BRST charges for complex systems

Two REDUCE programs implement the calculations

Discussion of specific solutions illustrates the method's effectiveness

Abstract

It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of {\tt REDUCE} are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.