# False Vacuum Decay in Gauge Theory

## TL;DR

This paper develops a gauge-invariant method to calculate the false vacuum decay rate in gauge theory, ensuring the result is independent of gauge parameters even after renormalization.

## Contribution

It provides a prescription for a one-loop calculation that yields a manifestly gauge-invariant decay rate in gauge theories.

## Key findings

- The decay rate is shown to be gauge-parameter independent after renormalization.
- A new prescription for gauge-invariant one-loop decay rate calculation is proposed.
- The method clarifies the gauge invariance of false vacuum decay in gauge theories.

## Abstract

The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $\xi$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.