QUANTUM KINEMATICS OF A TEST PARTICLE IN A CURVED SPACETIME

A possible model for the quantum kinematics of a test particle in curv ed spacetime is proposed. Every reasonable neighbourhood of a curved s pacetime can be equipped with a nonassociative binary operation called geodesic multiplication. Its infinitesimal right translations are use d to define the (geodesic) momentum operators. The corresponding commu tation relations are taken as the quantum kinematic algebra. It coinci des with the usual canonical Poisson algebra (Weyl's kinematics) only in the case of flat spacetime. A BRST-like operator is constructed and its physical meaning is discussed. As an example, detailed calculatio ns are performed for the spacetime of a weak plane gravitational wave.