We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in $3+1$ dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results show in particular that the quantum corrections strongly increase when one approaches the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.

• Received 30 July 2003

DOI:https://doi.org/10.1103/PhysRevD.69.025009