Incompressible Canonical Quantization

Abstract

The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based on this set of variables, the quantum mechanical description of the motion of a particle in a manifold, is identical to that associated with the familiar canonically conjugate variables xk and pk in an Euclidean space with Cartesian coordinates. The controversy related to non-uniqueness of momentum operators when the range of a coordinate is a finite interval is reduced to two possible extensions. This suggests relating these two types of extensions to the type of particle as being fermion or boson.