Hamilton relativity group for noninertial states in quantum mechanics

Physical states in quantum mechanics are rays in a Hilbert space. Projective representations of a relativity group transform between the quantum physical states that are in the admissible class. The physical observables of position, time, energy and momentum are the Hermitian representation of the Weyl-Heisenberg algebra. We show that there is a consistency condition that requires the relativity group to be a subgroup of the group of automorphisms of the Weyl-Heisenberg algebra. This, together with the requirement of the invariance of classical time, results in the inhomogeneous Hamilton group that is the relativity group for noninertial frames in classical Hamilton's mechanics. The projective representation of a group is equivalent to unitary representations of its central extension. The central extension of the inhomogeneous Hamilton group and its corresponding Casimir invariants are computed. One of the Casimir invariants is a generalized spin that is invariant for noninertial states. It is the familiar inertial Galilean spin with additional terms that may be compared to noninertial experimental results.