External gravitational interactions in quantum field theory

The renormalization of Green's functions of lambdaphi4 quantum field theory is considered in an external gravitational field specified by the metric tensor g/subu//subv/(y). Green's functions GAMMA(/subn//subj/= describing the interaction of j scalar particles to arbitrary order n in the gravitational field are shown to be made finite by the standard renormalizations of the flat space theory and a renormalization of the coefficient of the improvement term in the action functional. These results in phi4 theory can be extended to all renormalizable field theories