Linear spin-zero quantum fields in external gravitational and scalar fields

We give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in a stationary curved space-time. We show how, following Segal, Weinless etc., the problem reduces to finding a “one particle structure” for the corresponding classical system. Our main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are:

1. A discussion of when a given “equal-time” surface in a given stationary space-time is Cauchy.
2. A modification and extension of the methods of Chernoff 3] for proving the essential self-adjointness of certain partial differential operators.