Perturbative quantum gauge invariance: Where the ghosts come from

TL;DR

This paper presents a purely quantum approach to gauge invariance in quantum gauge theories, deriving classical gauge structures from quantum principles without classical starting points, using a free field BRST transformation.

Contribution

It introduces a quantum-based method to recover classical gauge structures directly from quantum principles, avoiding classical-to-quantum quantization procedures.

Findings

Classical gauge group structures can be derived from quantum principles.

The free BRST gauge transformation applies to various gauge theories.

The approach does not rely on path integral methods.

Abstract

A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories which are then subject to quantization, but it is also possible to recover the classical group structure and coupling properties from purely quantum mechanical principles. As a main tool we use a free field version of the Becchi-Rouet-Stora-Tyutin gauge transformation, which contains no interaction terms related to a coupling constant. This free gauge transformation can be formulated in an analogous way for quantum electrodynamics, Yang-Mills theories with massless or massive gauge bosons and quantum gravity.