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

TL;DR

This paper develops covariant path integrals for quantum fields interacting with classical spacetime, ensuring consistency, symmetry, and positivity, and proposes a covariant formulation of gravity that preserves quantum entanglement constraints.

Contribution

It introduces a covariant path integral framework for quantum-classical interactions, including a novel formulation of gravity that maintains covariance and positivity.

Findings

Path integrals can be constructed to be completely positive without master equations.

The framework respects space-time symmetries like Lorentz and diffeomorphism invariance.

Entanglement cannot be generated via classical fields, supporting quantum gravity tests.

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. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics. The theory is manifestly covariant, and may be inequivalent to the theory derived using master-equation methods. We prove that entanglement cannot be created via the classical field, reinforcing proposals to test the quantum nature of gravity via entanglement generation.