Quantum mechanics of a spin particle in a curved spacetime with absolute time

We present a new covariant approach to the quantum mechanics of a charged 12-spin particle in given electromagnetic and gravitational fields. The background space is assumed to be a curved Galilean spacetime, that is a curved spacetime with absolute time. This setting is intended both as a suitable approximation for the case of low speeds and feeble gravitational fields, and as a guide for eventual extension to fully Einsteinian spacetime. Moreover, in the flat spacetime case one completely recovers the standard non-relativistic quantum mechanics. ork is a generalization of [18], where the quantum mechanics of scalar particles was formulated within a similar approach.