ON THE STRUCTURE OF QUANTIZABLE ALGEBRAS OF THE PRODUCTS OF SYMPLECTIC MANIFOLDS WITH POLARIZATIONS

Abstract

A canonical polarization of symplectic product of two symplectic manifolds with polarization is constructed from the polarizations of each symplectic manifold. The polarizations is referred to as product polarization. The structure of quantizable algebras of symplectic products of two symplectic manifolds with respect to the product polarization in the sense of the geometric quantization is studied. The so-called GQ-consistent kinematical algebras of the products are extracted from the quantizable algebras.

Keywords :Quantization, Differential Geometry