This research falls under the broad headings of symplectic geometry and geometric quantization. In addition to its geometric content, it involves both algebraic theory and analysis; and aside from it purely mathematical interest, it is of considerable interest to mathematical physics. The research is divided into five topics: (1) the geometric quantization of the Marsden-Weinstein reduced phase spaces; (2) the geometric quantization of the symplectic tori; (3) symplectic spinors and half-forms for infinite-dimensional symplectic vector spaces and polarizations; (4) the structure and representation theory of the algebra generated by the canonical commutation relations in exponential form; and (5) the structure and representation theory of commutative Poisson algebras. This research is in the general area of geometric algebra and mathematical physics. Its aim is to investigate aspects of symplectic geometry, in particular aspects pertaining to geometric quantization.
