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

Understand

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.