  In a recent paper we quantized the interaction of gravity with a Yang-Mills
and Higgs field and obtained as a result a gravitational wave equation in a
globally hyperbolic spacetime. Assuming that the Cauchy hypersurfaces are
compact we proved a spectral resolution for the wave equation by applying the
method of separation of variables. In this paper we extend the results to the
case when the Cauchy hypersurfaces are non-compact by considering a Gelfand
triplet and applying the nuclear spectral theorem.
