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When classical degrees of freedom and quantum degrees of freedom areconsistently coupled, the former diffuse, while the latter undergo decoherence.Here, we construct a theory of quantum matter fields and Nordstrom gravity inwhich the space-time metric is treated classically. The dynamics is constructedvia the classical-quantum path integral and is completely positive, tracepreserving (CPTP), and respects the classical-quantum split. The weak fieldlimit of the model matches the Newtonian limit of the full covariant pathintegral but it is easier to show that the theory is both diffeomorphisminvariant, CPTP, and has the appropriate classical limit.

Diffeomorphism invariant classical-quantum path integrals for Nordstrom gravity