Proper BRST quantization of relativistic particles

TL;DR

This paper applies a formal BRST quantization method to relativistic particles with spin, deriving exact solutions and exploring implications for theories with graded gauge symmetries, despite challenges in Lorentz covariance.

Contribution

It introduces general quantization rules that turn formal BRST solutions into exact ones and extends their applicability to graded gauge theories.

Findings

Derived exact BRST solutions for relativistic particles.

Identified two inequivalent quantization procedures based on metric choices.

Provided insights into Lorentz covariance issues in inner product space quantization.

Abstract

Recently derived general formal solutions of a BRST quantization on inner product spaces of irreducible Lie group gauge theories are applied to trivial models and relativistic particle models for particles with spin 0, 1/2 and 1. In the process general quantization rules are discovered which make the formal solutions exact. The treatment also give evidence that the formal solutions are directly generalizable to theories with graded gauge symmetries. For relativistic particles reasonable results are obtained although there exists no completely Lorentz covariant quantization of the coordinate and momenta on inner product spaces. There are two inequivalent procedures depending on whether or not the time coordinate is quantized with positive or indefinite metric states. The latter is connected to propagators.