Covariant path integrals for quantum fields back-reacting on classical space-time

• URL: http://arxiv.org/abs/2302.07283v2
• Date: Wed, 15 Nov 2023 02:05:48 GMT
• Title: Covariant path integrals for quantum fields back-reacting on classical space-time
• Authors: Jonathan Oppenheim and Zachary Weller-Davies
• Abstract summary: We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the path integral of classical dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master equation methods. These path integrals allow one to readily impose space-time symmetries, including Lorentz invariance or diffeomorphism invariance. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the stochastic path integral of classical stochastic dynamics while respecting symmetry principles. We introduce a path integral formulation of general relativity where the space-time metric is treated classically, as well as a diffeomorphism invariant theory based on the trace of Einstein's equations. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics.

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