An Exact False Vacuum Decay Rate.

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 an complete decay rate after renormalization. We derive simple expansions in the thin and thick wall limits and investigate their validity.