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arXiv · 2312.07677

Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics

Z. Haba
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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.

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Z. Haba. 2024-08-29. Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics. https://doi.org/10.1209/0295-5075%2Fad64fe

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