The quantization of constrained systems: from symplectic reduction to Rieffel induction
| dc.creator | Landsman, N. P. | |
| dc.date | 1996-01-18 | |
| dc.date.accessioned | 2026-07-07T09:12:42Z | |
| dc.date.available | 2026-07-07T09:12:42Z | |
| dc.description | This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein and Xu. Secondly, it is shown how this procedure is quantized by Rieffel induction, a technique in operator algebra theory. The essential point is that a symplectic space with generalized moment map is quantized by a pre-(Hilbert) C^*-module. The connection with Dirac's constrained quantization method is explained. Three examples with a single constraint are discussed in some detail: the reduced space is either singular, or defined by a constraint with incomplete flow, or unproblematic but still interesting. In all cases, our quantization procedure may be carried out. Finally, we re-interpret and generalize Mackey's quantization on homogeneous spaces. This provides a double illustration of the connection between C^*-modules and the moment map. | |
| dc.description | 24 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9601009 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9601009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152107 | |
| dc.subject | Differential Geometry | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | The quantization of constrained systems: from symplectic reduction to Rieffel induction | |
| dc.type | text |