Diffeomorphism invariant classical-quantum path integrals for Nordström gravity

When classical degrees of freedom and quantum degrees of freedom are consistently coupled, the former diffuse, while the latter undergo decoherence. Here, we construct a theory of quantum matter fields and Nordström gravity in which the space-time metric is treated classically. The dynamics is constructed via the classical-quantum path integral and is completely positive, trace preserving (CPTP) and respects the classical-quantum split. The weak-field limit of the model matches the Newtonian limit of the full covariant path integral, but it is easier to show that the theory is both diffeomorphism invariant and CPTP and has the appropriate classical limit. Published by the American Physical Society 2024