Tunneling Potentials for the Tunneling Action: Gauge Invariance

TL;DR

This paper develops a gauge-invariant method for calculating tunneling rates at zero temperature using the tunneling potential approach, improving numerical efficiency while controlling gauge dependence.

Contribution

It introduces a gauge-invariant procedure for tunneling rate calculation within the tunneling potential framework, addressing gauge dependence issues.

Findings

The method achieves gauge invariance up to polynomial approximation errors.

Numerical efficiency surpasses standard bounce solution methods.

Residual gauge dependence is minimized and well-understood.

Abstract

We formulate a procedure to obtain a gauge-invariant tunneling rate at zero temperature using the recently developed tunneling potential approach. This procedure relies on a consistent power counting in gauge coupling and a derivative expansion. The tunneling potential approach, while numerically more efficient than the standard bounce solution method, inherits the gauge-dependence of the latter when naively implemented. Using the Abelian Higgs model, we show how to obtain a tunneling rate whose residual gauge-dependence arises solely from the polynomial approximations adopted in the tunneling potential computation.