A formal model of Berezin-Toeplitz quantization
| dc.creator | Karabegov, Alexander V. | |
| dc.date | 2006-07-15 | |
| dc.date | 2006-08-15 | |
| dc.date.accessioned | 2026-07-07T07:18:24Z | |
| dc.date.available | 2026-07-07T07:18:24Z | |
| dc.description | We give a new construction of symbols of the differential operators on the sections of a quantum line bundle $L$ over a Kaehler manifold $M$ using the natural contravariant connection on $L$. These symbols are the functions on the tangent bundle $TM$ polynomial on fibres. For high tensor powers of $L$, the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on $TM$ corresponding to some pseudo-Kaehler structure on $TM$. Surprisingly, this star product is intimately related to the formal symplectic groupoid with separation of variables over $M$. We extend the star product on $TM$ to generalized functions supported on the zero section of $TM$. The resulting algebra of generalized functions contains an idempotent element which can be thought of as a natural counterpart of the Bergman projection operator. Using this idempotent, we define an algebra of Toeplitz elements and show that it is naturally isomorphic to the algebra of Berezin-Toeplitz deformation quantization on $M$. | |
| dc.description | 36 pages, a minor mistake is corrected | |
| dc.identifier | https://arxiv.org/abs/math/0607365 | |
| dc.identifier | http://arxiv.org/abs/math/0607365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114289 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 53D55 | |
| dc.title | A formal model of Berezin-Toeplitz quantization | |
| dc.type | text |