Convexity, gauge-dependence and tunneling rates

TL;DR

This paper demonstrates that tunneling and nucleation rates in quantum field theory are gauge-independent despite the gauge dependence of the effective action, by analyzing the role of the false vacuum effective action and Nielsen identities.

Contribution

It clarifies the relationship between gauge dependence, convexity, and tunneling rates, showing that decay rates are gauge-independent and determined by a non-convex effective action evaluated at a generalized bounce.

Findings

Tunneling rates are gauge-independent despite gauge-dependent effective actions.

Decay rates are determined by a non-convex false vacuum effective action at an extremum.

Gauge-independence follows from Nielsen identities for invertible Faddeev-Popov matrices.

Abstract

We clarify issues of convexity, gauge-dependence and radiative corrections in relation to tunneling rates. Despite the gauge dependence of the effective action at zero and finite temperature, it is shown that tunneling and nucleation rates remain independent of the choice of gauge-fixing. Taking as a starting point the functional that defines the transition amplitude from a false vacuum onto itself, it is shown that decay rates are exactly determined by a non-convex, false vacuum effective action evaluated at an extremum. The latter can be viewed as a generalized bounce configuration, and gauge-independence follows from the appropriate Nielsen identities. This holds for any election of gauge-fixing that leads to an invertible Faddeev-Popov matrix.