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. 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 .1

We present a regularized and renormalized version of the one-loop nonlinear relaxation equations that determine the nonequilibrium time evolution of a classical ͑constant͒ 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 4 theory; the results are similar to the ones found previously by other groups. ͓S0556-2821͑97͒04104-0͔

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.

We present an evaluation of the one-loop prefactor in the lifetime of a metastable state which decays at finite temperature by bubble nucleation. Such a state is considered in the one-component (p4 model in three space dimensions. The calculation serves as a prototype application of a fast numerical method for evaluating the functional determixiants that appear in semiclassical approximations. PACS number(s): 98.80. Hw, 03.70.+k, 64.60.Qb

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 previously assumed, 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.1