Star-polarization: A natural link between phase space representation and operator representation of quantum mechanics

Abstract

The method of *-polarization connects phase space mechanics to the usual operator formulation of quantum theory. A *-polarization is a linear submanifold of the space of C ^∞ functions on phase space. Elements of a *-polarization are in direct correspondence with the Schroedinger wave functions and this correspondence induces the Weyl correspondence between classical observables and operators. All generalized Moyal algebras admit *-polarizations and a general method is thus available for translating *-quantization into operator language.