Perturbative quantum gauge invariance: where the ghosts come from

Abstract

A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework, with path-integral methods used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories that are then subject to quantization: it is possible, instead, 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. PACS Nos.: 11.10.–z, 11.15.Bt, 12.20.Ds, 12.38.Bx