Deformation Quantization for Actions of R(d)

Erscheinungsjahr 1993
ISBN: 978-0-8218-2575-4
Verlag: American Mathematical Society

Buch, Englisch, 93 Seiten, Format (B × H): 180 mm x 255 mm

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.

This is a description of a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of Rd on that manifold.

Autoren/Hrsg.

Rieffel, Marc A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie