Quantum frames of reference

The present paper addresses itself to the problem of finite mass quantum frames of reference. We show that with the help of suitable geometrical potentials it is possible to construct a theory that takes account of the quantum disturbances of the reference frame in a consistent manner. We thus obtain a description of a physical system relative to reference frames described by the most general quantum states, within the framework of non relativistic theory. Our formalism satisfies an equivalence principle which presents an extension of the classical equivalence principle to quantum theory. It also augments the usual continuous Galilean symmetry with additional discrete symmetries corresponding to the transformation from one physical reference frame to another. (author)