Scalar quantum field in an external gravitational field

We consider a class of Lorentz metrics on IR⁴ which are Minkowskian off a compact set. For each such metric we construct a quantum field operator which satisfies the generalization of the Klein-Gordon equation. The field has a causal commutator and transforms as a scalar under general coordinate transformations. The field determines a unitary scattering operator which is invariant under coordinate transformations.