  The basic properties of Poincare gauge invariant Hilbert bundles over
Lorentzian manifolds are derived. Quantum connections are introduced in such
bundles, which govern a parallel transport that is shown to satisfy the strong
equivalence principle in the quantum regime. Path-integral expressions are
presented for boson propagators in Hilbert bundles over globally hyperbolic
curved spacetimes. Their Poincare gauge covariance is proven, and their special
relativistic limit is examined. A method for explicitly computing such
propagators is presented for the case of cosmological models with
Robertson-Walker metric.
