We now turn to the quantum mechanics of a point particle in a general metric-affine space. We first consider the path integral in a flat space with Cartesian coordinates
where is an abbreviation for the short-time amplitude
with . A possible external potential has been omitted since this would contribute in an additive way, uninfluenced by the space geometry.
Our basic postulate is that the path integral in a general metric-affine space should be obtained by an appropriate nonholonomic transformation of the amplitude (92) to a space with curvature and torsion.