False vacuum decay by self-consistent bounces in four dimensions

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.

45 pages, 9 figures

References in corpus (4)

• Oscillating bounce solutions and vacuum tunneling in de Sitter spacetime
• Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay
• One-loop fermionic corrections to the instanton transition in two dimensional chiral Higgs model
• Self-consistent bounces in two dimensions

Cited by in corpus (9)

• Effective field theory approach to thermal bubble nucleation
• Self-consistent solitons for vacuum decay in radiatively generated potentials
• Green's function method for handling radiative effects on false vacuum decay
• From QFT to Boltzmann: Freeze-in in the presence of oscillating condensates
• False vacuum decay rates, more precisely
• False vacuum decay beyond the quadratic approximation: summation of non-local self-energies
• Self-consistent radiative corrections to false vacuum decay
• Fate of homogeneous ${\mathbb{Z}}_2$-symmetric scalar condensates
• An application of the renormalization group to the calculation of the vacuum decay rate in flat and curved space-time