Quantum and Classical Gauge Symmetries

TL;DR

This paper explores the relationship between mass terms in gauge theories and gauge fixing, showing that mass terms can be interpreted as gauge fixing terms, which has implications for understanding massive gauge particles and gauge invariance.

Contribution

It demonstrates that the use of mass terms as gauge fixing is equivalent to the Faddeev-Popov method without large mass limits, offering a new perspective on gauge invariance and massive vector theories.

Findings

Mass terms can be viewed as gauge fixing terms.

Classical massive vector theories can be reinterpreted as gauge invariant.

Implications for the understanding of Higgs mechanism and gauge symmetry.

Abstract

The use of the mass term of the gauge field as a gauge fixing term, which was discussed by Zwanziger, Parrinello and Jona-Lasinio in a large mass limit, is related to the non-linear gauge by Dirac and Nambu. We have recently shown that this use of the mass term as a gauge fixing term is in fact identical to the conventional local Faddeev-Popov formula without taking a large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit. This suggests that the classical massive vector theory, for example, could be re-interpreted as a gauge invariant theory with a gauge fixing term added in suitably quantized theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge invariant, has a more intrinsic meaning. We comment on several implications of this observation.