Star-product quantization as an autonomous quantum theory is reviewed with emphasis on its relation to path integral and Hilbert space formulations. Quantization of the usual Heisenberg group is used as an example. When phase space is the cylinder, this group is replaced by E(2), the Euclidean group in two dimensions. This case is worked out in detail. In doing so, polarizations on the cylinder are discussed and a phase space path integral is constructed.

No abstract

No abstract