Quantization in Spaces of Constant Curvature

Abstract

A critique of the conventional canonical quantization method is given. In its place an alternative quantization scheme applicable to any complete Riemannian manifold of constant curvature is presented. The scheme is based firstly on a rigorous quantization of every momentum observable associated with a one-parameter group of transformations of the manifold, and secondly on a consideration of spatial symmetries and conservation laws. The formulation is coordinate independent and the troublesome generalized momenta no longer play any dominant role. Explicit examples are worked out leading to interesting results.