BRST Field Theory of Relativistic Particles

TL;DR

This paper introduces a generalized BRST field theory framework for relativistic particles, addressing quantization and gauge fixing, and reveals that naive formulations may lead to trivial quantum theories.

Contribution

It proposes a new generalized BRST field theory based on modified wave operators, applicable to relativistic particles and string theories, improving understanding of their quantization.

Findings

Generalized theories are relevant to BDHP relativistic particle formulations

Naive BRST formulations can lead to trivial quantum field theories

The paper discusses quantization, gauge fixing, and propagators in the new framework

Abstract

A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. We discuss their quantization, gauge fixing and the derivation of propagators. We show, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions.