  We discuss an exact false vacuum decay rate at one loop for a real and
complex scalar field in a quartic-quartic potential with two tree-level minima.
The bounce solution is used to compute the functional determinant from both
fluctuations. We obtain the finite product of eigenvalues and remove
translational zero modes. The orbital modes are regularized with the zeta
function and we end up with a complete renormalized decay rate. We derive
simple expansions in the thin and thick wall limits and determine their
validity.
