Stochastic quantum field dynamics in the proper time

Abstract

We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic wave function whose dynamics is determined by a non-linear Schr\"odinger-type evolution equation in an additional time parameter. The correct classical limit requires the proper time interpretation of the time parameter. An average over the proper time leads to the conventional quantum field theory of particles which are free at an infinite space separation. We consider models with scalar and vector fields on a pseudoriemannian manifold. A quantization of the Einstein gravity in this approach is briefly discussed.