Carsten Patzold

We consider the time evolution of systems in which a spatially homogeneous scalar field is coupled to fermions. The quantum back-reaction is taken into account in one-loop approximation. We set up the basic equations and their renormalization in a form suitable for numerical computations. The initial singularities appearing in the renormalized equations are removed by a Bogoliubov transformation. The equations are then generalized to those in a spatially flat Friedmann-Robertson-Walker universe. We have implemented the Minkowski space equations numerically and present results for the time evolution with various parameter sets. We find that fermion fluctuations are not in general as ineffective as assumed previously but show interesting features which should be studied further. In an especially interesting example we find that fermionic fluctuations can ``catalyze'' the evolution of bosonic fluctuations.

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.

We generalize a previously proposed renormalization and computation scheme for nonequilibrium dynamics to include finite temperature and one-loop selfconsistency as arising in the large-N limit. Since such a scheme amounts essentially to tadpole summation, it also includes, at high temperature, the hard mass corrections proportional to T^2. We present some numerical examples at T=0 and at finite temperature; the results reproduce the essential features of other groups. Especially, we can confirm a recently discovered sum rule for the late time behaviour.

Imposing initial conditions to nonequilibrium systems at some time t_0 leads, in renormalized quantum field theory, to the appearance of singularities in the variable t-t_0 in relevant physical quantities, such as energy density and pressure. The origin of these `initial singularities' can be traced back to the choice of initial state. We construct here, by a Bogoliubov transformation, initial states such that these singularities are eliminated. While the construction is not unique it can be considered a minimal way of taking into account the nonequilibrium evolution of the system prior to t_0.

We derive the renormalized nonequilibrium equations of motion for a scalar field and its quantum back reaction in a conformally flat Friedmann-Robertson-Walker universe. We use a fully covariant formalism proposed by us recently for handling numerically and analytically nonequilibrium dynamics in one-loop approximation. The system is assumed to be in a conformal vacuum state initially. We use dimensional regularization; we find that the counter terms can be chosen independent of the initial conditions though the divergent leading order graphs do depend on them.

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.