Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization
| dc.creator | Andersen, Jorgen Ellegaard | |
| dc.date | 2006-11-06 | |
| dc.date | 2008-03-13 | |
| dc.date.accessioned | 2026-07-07T09:26:27Z | |
| dc.date.available | 2026-07-07T09:26:27Z | |
| dc.description | We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove that Hitchin's connection induces a unique formal connection on smooth functions on the symplectic manifold. Parallel transport of this formal connection produces equivalences between the corresponding Berezin-Toeplitz deformation quantizations. - In the cases where the Hitchin connection is projectively flat, the formal connections will be flat and we get a symmetry-invariant formal quantization. If a certain cohomological condition is satisfied a global trivialization of this algebra bundle is constructed. As a corollary we get a symmetry-invariant deformation quantization. Finally, these results are applied to the moduli space situation in which Hitchin's originally constructed his connection. First we get a proof that the Hitchin connection in this case is the same as the connection constructed by Axelrod, Della Pietra and Witten. Second we obtain in this way a mapping class group invariant formal quantization of the smooth symplectic leaves of the moduli space of flat SU(n)-connections on any compact surface. | |
| dc.description | Typo's corrected | |
| dc.identifier | https://arxiv.org/abs/math/0611126 | |
| dc.identifier | http://arxiv.org/abs/math/0611126 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156758 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization | |
| dc.type | text |