False Vacuum Decay in Gauge Theory

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.