ORDERING PROBLEM IN QUANTUM-MECHANICS - PRIME QUANTIZATION AND A PHYSICAL INTERPRETATION

A method for quantizing a classical system, based upon the notion of localization on phase space, is developed. This method, to which is given the name ′ quantization, is based upon the mathematical theory of positive-operator-valued measures and their relationship to reproducing kernel Hilbert spaces, and to a notion of generalized kinematical variables related to phase space. For a system with openRn as its configuration space, it has the advantage of being able to connect the well-known problem of ordering in quantum mechanics to the choice of a measuring apparatus in a joint measurement of position and momentum (within the limits of the uncertainty principle). Moreover, for such a system, a choice of ordering in the present context also turns out to be a choice of polarization in the method of geometric quantization. © 1990 The American Physical Society.