Quantum back reaction in scalar QED as an initial-value problem

An initial-value formulation of the quantum back-reaction problem in scalar QED is presented. The semiclassical, mean-field limit of the theory for spatially homogeneous initial states yields (after renormalization) a tractable set of finite, coupled ordinary differential equations for the time evolution of the system. These equations describe the effects of particle creation and the associated induced electric current on the decay of a uniform background electric field, in a form suitable for implementation on a computer. The renormalization techniques and formulation of the initial-value problem employed provide a model for the numerical attack on the analogous back-reaction problem, involving fully interacting fields, in early Universe quantum cosmology.