Self-consistent bounces in two dimensions

TL;DR

This paper computes self-consistent bounce solutions for false vacuum decay in a two-dimensional Phi^4 model using the Hartree approximation, improving upon one-loop corrections by employing a spectral method for functional determinants.

Contribution

It introduces a numerical method that avoids spectrum discretization by using zero energy mode functions, and applies the 2PPI renormalization scheme for self-consistent decay rate calculations.

Findings

Corrections to the one-loop decay rate are relatively small, not exceeding an order of magnitude.

The iterative solution converges within a certain parameter range.

The spectral method simplifies the computation of functional determinants in bounce solutions.

Abstract

We compute bounce solutions describing false vacuum decay in a Phi**4 model in two dimensions in the Hartree approximation, thus going beyond the usual one-loop corrections to the decay rate. We use zero energy mode functions of the fluctuation operator for the numerical computation of the functional determinant and the Green's function. We thus avoid the necessity of discretizing the spectrum, as it is necessary when one uses numerical techniques based on eigenfunctions. Regularization is performed in analogy of standard perturbation theory; the renormalization of the Hartree approximation is based on the two-particle point-irreducible (2PPI) scheme. The iteration towards the self-consistent solution is found to converge for some range of the parameters. Within this range we find the corrections to the leading one-loop approximation to be relatively small, not exceeding one order of magnitude in the total transition rate.