False vacuum decay exact computation of the classical bounce

Abstract

This thesis reviews the exact numerical computation of the classical bounce solution in the false vacuum decay for a quartic scalar eld potential which is o set by an external source. The decay rate in a semiclassical analysis consists of a leading exponential contribution due to the classical action evaluated on the classical bounce solution as well as a prefactor of functional determinants due to quantum uctuations about the classical bounce solution. The equation of motion of the classical bounce solution is obtained using the Euler-Lagrange equation and is numerically solved using the shooting method and the nite-di erence method. The appendix reviews a computational technique for evaluating the functional determinants of one-dimensional operators via the Gel'fand- Yaglom theorem.