False vacuum decay by self-consistent bounces in four dimensions

TL;DR

This paper develops a method to compute self-consistent bounce solutions for false vacuum decay in a four-dimensional Phi^4 model, incorporating quantum back-reaction effects beyond the semiclassical approximation, and analyzes their impact on decay rates.

Contribution

It introduces a self-consistent approach to include quantum back-reaction in bounce solutions, improving upon traditional semiclassical methods in four-dimensional models.

Findings

Corrections to the semiclassical action are a few percent.

Transition rate corrections can be several orders of magnitude.

Self-consistent solutions exist within a parameter range, with deviations increasing at large couplings.

Abstract

We compute bounce solutions describing false vacuum decay in a Phi**4 model in four dimensions with quantum back-reaction. The back-reaction of the quantum fluctuations on the bounce profiles is computed in the one-loop and Hartree approximations. This is to be compared with the usual semiclassical approach where one computes the profile from the classical action and determines the one-loop correction from this profile. The computation of the fluctuation determinant is performed using a theorem on functional determinants, in addition we here need the Green' s function of the fluctuation operator in oder to compute the quantum back-reaction. As we are able to separate from the determinant and from the Green' s function the leading perturbative orders, we can regularize and renormalize analytically, in analogy of standard perturbation theory. The iteration towards self-consistent solutions is found to converge for some range of the parameters. Within this range the corrections to the semiclassical action are at most a few percent, the corrections to the transition rate can amount to several orders of magnitude. The strongest deviations happen for large couplings, as to be expected. Beyond some limit, there are no self-consistent bounce solutions.