QUANTUM MECHANICS AND PATH INTEGRALS IN SPACES WITH CURVATURE AND TORSION

Abstract

We point out that there is a natural geometric procedure for constructing the quantum theory of a particle in a general metric-affine space with curvature and torsion. Quantization rules are presented and expressed in the form of a simple path integral formula which specifies compactly a new combined equivalence and correspondence principle. The associated Schrödinger equation has no extra curvature nor torsion terms that have plagued earlier attempts. Several well-known physical systems are invoked to suggest the correctness of the proposed theory.