Reduction and quantization for singular momentum mappings

✍ Scribed by Jedrzej Śniatycki; Alan Weinstein

• Publisher: Springer
• Year: 1983
• Tongue: English
• Weight: 289 KB
• Volume: 7
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00419934

✦ Synopsis

When a Hamiltonian action of Lie group on a symplectic manifold has a singular momentum mapping, the reduced manifold may not exist. Nevertheless, we may always construct a Poisson algebra which corresponds to the functions on the reduced manifold in the regular case. The ideas of geometric quantization are extended to Poisson algebras, and it is shown in an example that quantization may be carried out before or after reduction, with isomorphic results.