  Dynamical evolution is described as a parallel section on an infinite
dimensional Hilbert bundle over the base manifold of all frames of reference.
The parallel section is defined by an operator-valued connection whose
components are the generators of the relativity group acting on the base
manifold. In the case of Galilean transformations we show that the property
that the curvature for the fundamental connection must be zero is just the
Heisenberg equations of motion and the canonical commutation relation in
geometric language. We then consider linear and circular accelerating frames
and show that pseudo-forces must appear naturally in the Hamiltonian.
