  We develop a unified formalism for describing the interaction of
gravitational waves with matter that clearly separates the effects of general
relativity from those due to interactions in the matter. Using it, we derive a
general expression for the dispersion of gravitational waves in matter in terms
of correlation functions for the matter in flat spacetime. The self energy of a
gravitational wave is shown to have contributions analogous to the paramagnetic
and diamagnetic contributions to the self energy of an electromagnetic wave. We
apply the formalism to some simple systems - free particles, an interacting
scalar field, and a fermionic superfluid.
