Classical wave operators and asymptotic quantum field operators on curved space-times

We consider a class of Lorentzian metrics on R4 which are stationary at time-like infinity and Minkowskian either at space-like or time-like infinity. For these metrics, we construct wave operators for the classical Klein-Gordon equation. For certain transient cases we also construct inverse wave operators. Given the classical wave operators, we show how to construct in and out field operators for the quantum Klein-Gordon equation and a particle interpretation for this theory. Finally, we give several results of a general nature on the construction of classical and quantum scattering operators paying special attention to the stationary case. The methods and results of the paper could be generalized to other external field problems (not just gravitational)