On the relation between geometric and deformation quantization
| dc.creator | Nölle, Christoph | |
| dc.date | 2008-09-11 | |
| dc.date.accessioned | 2026-07-07T10:02:13Z | |
| dc.date.available | 2026-07-07T10:02:13Z | |
| dc.description | In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the ordinary pointwise product of functions, whereas geometric quantization is a prescription for the construction of a Hilbert space and a few quantum operators, starting from a symplectic manifold. We determine under which conditions it is possible to define a representation of the deformed algebra on this Hilbert space, thereby to extend the small class of quantizable observables in geometric quantization to all smooth functions, as well as to give a natural representation of the algebra. In particular we look at the special cases of a cotangent bundle and a Kähler manifold. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0809.1946 | |
| dc.identifier | http://arxiv.org/abs/0809.1946 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168897 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the relation between geometric and deformation quantization | |
| dc.type | text |