Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics
arXiv:2312.07677 · doi:10.1209/0295-5075/ad64fe
Abstract
We study the quantum field theory (QFT) of a scalar field in the Schrödinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We discuss a transition between Riemannian and pseudoRiemannian metrics (signature inversion). We express the real time Schrödinger evolution by the Brownian motion . We discuss the Feynman integral for a scalar field in a radiation background. We show that the unitary Schrödinger evolution for positive time can go over for negative time into a dissipative evolution described by diffusive paths.
15 pages