Deformation Quantization for Actions of $R^d$

Download or read book Deformation Quantization for Actions of $R^d$ written by Marc Aristide Rieffel and published by American Mathematical Soc.. This book was released on 1993 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.