Pseudoforces in quantum mechanics - art. no. 042107

Dynamical evolution is described as a parallel section on an infinite-dimen sional Hilbert bundle over the base manifold of all frames of reference. Th e parallel section is defined by an operator-valued connection whose compon ents are the generators of the relativity group acting on the base manifold . In the case of Galilean transformations we show that the property that th e curvature for the fundamental connection must be zero is just the Heisenb erg equations of motion and the canonical commutation relation in geometric language. We then consider linear and circular accelerating frames and sho w that pseudoforces must appear naturally in the Hamiltonian.