# On the Gauge Invariance of the Decay Rate of False Vacuum

## TL;DR

This paper develops a systematic, gauge-invariant method to calculate the decay rate of false vacuum in models where the scalar field carries gauge charge, addressing gauge dependence issues in such decay processes.

## Contribution

It introduces a new, systematic approach to perform gauge-invariant calculations of false vacuum decay rates in gauge theories.

## Key findings

- Derived a manifestly gauge-invariant formula for decay rate
- Provided a systematic method for integrating out gauge field fluctuations
- Ensured gauge invariance in false vacuum decay calculations

## Abstract

We study the gauge invariance of the decay rate of the false vacuum for the model in which the scalar field responsible for the false vacuum decay has gauge quantum number. In order to calculate the decay rate, one should integrate out the field fluctuations around the classical path connecting the false and true vacua (i.e., so-called bounce). Concentrating on the case where the gauge symmetry is broken in the false vacuum, we show a systematic way to perform such an integration and present a manifestly gauge-invariant formula of the decay rate of the false vacuum.