Schr\"odinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics
Abstract
We study the quantum field theory (QFT) of a scalar field in the Schr\"odinger 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 Schr\"odinger evolution by the Brownian motion . We discuss the Feynman integral for a scalar field in a radiation background. We show that the unitary Schr\"odinger evolution for positive time can go over for negative time into a dissipative evolution described by diffusive paths.
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