  This paper summarizes and generalizes a recently proposed mathematical
framework that unifies the standard formalisms of special relativity and
quantum mechanics. The framework is based on Hilbert spaces H of functions of
four space-time variables x,t, furnished with an additional indefinite inner
product invariant under Poincar\'e transformations, and isomorphisms of these
spaces that preserve the indefinite metric. The indefinite metric is
responsible for breaking the symmetry between space and time variables and for
selecting a family of Hilbert subspaces that are preserved under Galileo
transformations. Within these subspaces the usual quantum mechanics with
Schr\"odinger evolution and t as the evolution parameter is derived.
Simultaneously, the Minkowski space-time is isometrically embedded into H,
Poincar\'e transformations have unique extensions to isomorphisms of H and the
embedding commutes with Poincar\'e transformations. The main new result is a
proof that the framework accommodates arbitrary pseudo-Riemannian space-times
furnished with the action of the diffeomorphism group.
