Self-consistent bounces in two dimensions

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.Comment: 30 pages, 12 figure

One-loop corrections to the metastable vacuum decay

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self interacting scalar field in 3+1 dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results in particular show that quantum corrections become smaller away from the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.Comment: 31 pages, 7 figure

Nonequilibrium dynamics: a renormalized computation scheme

We present a regularized and renormalized version of the one-loop nonlinear relaxation equations that determine the non-equilibrium time evolution of a classical (constant) field coupled to its quantum fluctuations. We obtain a computational method in which the evaluation of divergent fluctuation integrals and the evaluation of the exact finite parts are cleanly separated so as to allow for a wide freedom in the choice of regularization and renormalization schemes. We use dimensional regularization here. Within the same formalism we analyze also the regularization and renormalization of the energy-momentum tensor. The energy density serves to monitor the reliability of our numerical computation. The method is applied to the simple case of a scalar phi^4 theory; the results are similar to the ones found previously by other groups.Comment: 15 pages, 9 postscript figures, revtex; version published in Phys. Rev, with minor corrections; improves the first version of 1996 by including the discussion of energy momentum tenso

The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.Comment: 19 pages, 9 figures; v2: references added, some changes in the tex

Nonequilibrium dynamics: preheating in the SU(2) Higgs model

The term `preheating' has been introduced recently to denote the process in which energy is transferred from a classical inflaton field into fluctuating field (particle) degrees of freedom without generating yet a real thermal ensemble. The models considered up to now include, besides the inflaton field, scalar or fermionic fluctuations. On the other hand the typical ingredient of an inflationary scenario is a nonabelian spontaneously broken gauge theory. So the formalism should also be developed to include gauge field fluctuations excited by the inflaton or Higgs field. We have chosen here, as the simplest nonabelian example, the SU(2) Higgs model. We consider the model at temperature zero. From the technical point of view we generalize an analytical and numerical renormalized formalism developed by us recently to coupled channnel systems. We use the 't Hooft-Feynman gauge and dimensional regularization. We present some numerical results but reserve a more exhaustive discussion of solutions within the paramter space of two couplings and the initial value of the Higgs field to a future publication.Comment: 30 pages, 10 figures in enhanced postscript, 2 unreadable figures made accessibl

Out-of-equilibrium evolution of scalar fields in FRW cosmology: renormalization and numerical simulations

We present a renormalized computational framework for the evolution of a self-interacting scalar field (inflaton) and its quantum fluctuations in an FRW background geometry. We include a coupling of the field to the Ricci scalar with a general coupling parameter $\xi$. We take into account the classical and quantum back reactions, i.e., we consider the the dynamical evolution of the cosmic scale factor. We perform, in the one-loop and in the large-N approximation, the renormalization of the equation of motion for the inflaton field, and of its energy momentum tensor. Our formalism is based on a perturbative expansion for the mode functions, and uses dimensional regularization. The renormalization procedure is manifestly covariant and the counter terms are independent of the initial state. Some shortcomings in the renormalization of the energy-momentum tensor in an earlier publication are corrected. We avoid the occurence of initial singularities by constructing a suitable class of initial states. The formalism is implemented numerically and we present some results for the evolution in the post-inflationary preheating era.Comment: 44 pages, uses latexsym, 6 pages with 11 figures in a .ps fil

Parton distributions in the chiral quark model: a continuum computation

We compute the parton distributions for the chiral quark model. We present a new technique for performing such computations based on Green functions. This approach avoids a discretization of the spectrum. It therefore does not need any smoothing procedures. The results are similar to those of other groups, however the distributions peak at smaller $x$.Comment: 19 pages, 8 Figures, LaTeX, some typos corrected, some additional comments in the conclusion

Renormalization of the nonequilibrium dynamics of fermions in a flat FRW universe

We derive the renormalized equations of motion and the renormalized energy-momentum tensor for fermions coupled to a spatially homogeneous scalar field (inflaton) in a flat FRW geometry. The fermion back reaction to the metric and to the inflaton field is formulated in one-loop approximation. Having determined the infinite counter terms in an $\bar{MS}$ scheme we formulate the finite terms in a form suitable for numerical computation. We comment on the trace anomaly which is inferred from the standard analysis. We also address the problem of initial singularities and determine the Bogoliubov transformation by which they are removed.Comment: 26 pages, LaTe

Out-of-equilibrium evolution of quantum fields in the hybrid model with quantum back reaction

The hybrid model with a scalar "inflaton" field coupled to a "Higgs" field with a broken symmetry potential is one of the promising models for inflation and (p)reheating after inflation. We consider the nonequilibrium evolution of the quantum fields of this model with quantum back reaction in the Hartree approximation, in particular the transition of the Higgs field from the metastable "false vacuum" to the broken symmetry phase. We have performed the renormalization of the equations of motion, of the gap equations and of the energy density, using dimensional regularization. We study the influence of the back reaction on the evolution of the classical fields and of the quantum fluctuations. We observe that back reaction plays an important role over a wide range of parameters. Some implications of our investigation for the preheating stage after cosmic inflation are presented.Comment: 35 pages, 16 eps figures, revtex4; v2: typos corrected and references added, accepted for publication in Physical Review

Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a symmetric and a double well potential. We use the 2PPI formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field phi= the 2PPI formalism uses as variational parameter a time dependent mass M**2(t) which contains all local insertions into the Green function. We compare our results to those obtained in the Hartree approximation. In the symmetric Phi**4 theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in 1+1 dimensional quantum field theory there is no spontaneous symmetry breaking for T >0, and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.Comment: 14 pages, 18 encapsulated postscript figures; v2 minor changes, new appendix, accepted for publication in Phys.Rev.