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. 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.