This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of R]d on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.
Series: Memoirs of the American Mathematical Society
Number Of Pages: 93
Published: January 1993
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 25.4 x 18.42
Weight (kg): 0.2