# 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 »

- Authors:

- Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund (Germany)
- (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}

}