Nonequilibrium dynamics: A renormalized computation scheme

We present a regularized and renormalized version of the one-loop nonlinear relaxation equations that determine the nonequilibrium 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.