  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.
