C*-algebraic quantization and the origin of topological quantum effects

✍ Scribed by N. P. Landsman

• Book ID: 104766679
• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 459 KB
• Volume: 20
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00417225

✦ Synopsis

Concepts from the theory of abstract operator algebras are used to solve the problem of quantizing a particle moving on an arbitrary locally compact homogeneous space. Inequivalent quantizations are identified with inequivalent irreducible representations of the corresponding C*-algebra. Topological terms in the action (or Hamiltonian) are found to be representation-dependent, and are automatically induced by the quantization procedure. Known charge quantization conditions turn out to be identically satisfied. Several examples are considered, among them the Dirac monopole and the Aharonov-Bohm effect.