False vacuum decay rates, more precisely

TL;DR

This paper presents a new method for precisely calculating vacuum decay rates in scalar field theories, incorporating quantum and gradient effects beyond the thin-wall approximation at the one-loop level.

Contribution

It introduces a technique to compute decay rates that includes quantum corrections and gradient effects, improving accuracy over previous thin-wall approximations.

Findings

Efficient calculation of functional determinants using Gel'fand-Yaglom method.

Inclusion of quantum and gradient effects in decay rate computations.

Application to scalar field theories beyond the thin-wall regime.

Abstract

We develop a method for accurately calculating vacuum decay rates beyond the thin-wall regime in a pure scalar field theory at the one-loop level of the effective action. It accounts for radiative effects resulting from quantum corrections to the classical bounce, including gradient effects stemming from the inhomogeneity of the bounce background. To achieve this, it is necessary to compute not only the functional determinant of the fluctuation operator in the background of the classical bounce but also its functional derivative evaluated at the classical bounce. The former is efficiently calculated using the Gel'fand-Yaglom method. We illustrate how the latter can also be calculated with the same method, combined with a computation of various Green's functions.