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Title: False vacuum decay by self-consistent bounces in four dimensions

Abstract

We compute bounce solutions describing false vacuum decay in a {phi}{sup 4} model in four dimensions with quantum backreaction. The backreaction 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 backreaction. As we are able to separate from the determinant and from the Gree n'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. The transition rates are reduced for the one-loop backreaction, for the Hartree backreaction they are reduced for {alpha}more » < or approx. 0.5 and enhanced for larger values of {alpha}. Beyond some limit, there are no self-consistent bounce solutions.« less

Authors:
;  [1];  [2]
  1. Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund (Germany)
  2. (Germany) and Andronikashvili Institute of Physics, GAS, 0177 Tbilisi (Georgia)
Publication Date:
OSTI Identifier:
21011094
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.045001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; CORRECTIONS; FLUCTUATIONS; GREEN FUNCTION; HARTREE-FOCK METHOD; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; PHI4-FIELD THEORY; RENORMALIZATION; SEMICLASSICAL APPROXIMATION

Citation Formats

Baacke, Juergen, Kevlishvili, Nina, and Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund. False vacuum decay by self-consistent bounces in four dimensions. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.045001.
Baacke, Juergen, Kevlishvili, Nina, & Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund. False vacuum decay by self-consistent bounces in four dimensions. United States. doi:10.1103/PHYSREVD.75.045001.
Baacke, Juergen, Kevlishvili, Nina, and Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund. Thu . "False vacuum decay by self-consistent bounces in four dimensions". United States. doi:10.1103/PHYSREVD.75.045001.
@article{osti_21011094,
title = {False vacuum decay by self-consistent bounces in four dimensions},
author = {Baacke, Juergen and Kevlishvili, Nina and Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund},
abstractNote = {We compute bounce solutions describing false vacuum decay in a {phi}{sup 4} model in four dimensions with quantum backreaction. The backreaction 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 backreaction. As we are able to separate from the determinant and from the Gree n'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. The transition rates are reduced for the one-loop backreaction, for the Hartree backreaction they are reduced for {alpha} < or approx. 0.5 and enhanced for larger values of {alpha}. Beyond some limit, there are no self-consistent bounce solutions.},
doi = {10.1103/PHYSREVD.75.045001},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • We compute bounce solutions describing false vacuum decay in a {phi}{sup 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 scheme. The iteration towards themore » 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 1 order of magnitude in the total transition rate.« less
  • The probability of destruction of a metastable vacuum state by the field of a highly virtual particle with energy [ital E] is calculated for a (3+1)-dimensional theory in the leading WKB approximation in the thin-wall limit. It is found that the induced nucleation rate of bubbles, capable of expansion, is exponentially small at any energy. The negative exponential power in the rate reaches its maximum at the energy, corresponding to the top of the barrier in the bubble energy, where it is a finite fraction of the same power in the probability of the spontaneous decay of the false vacuum,more » i.e., at [ital E]=0.« less
  • We consider two-dimensional scalar theories with two vacuum states. The vacuum built on the local minimum of the field potential (the so-called false one) is known to decay spontaneously through quantum tunneling. A collision of two particles at energy {radical}{ital s} is shown to increase exponentially the decay probability like a single particle of mass {radical}{ital s} .
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