  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.
