Deformation quantization of submanifolds and reductions via Duflo-Kirillov-Kontsevich map
| dc.creator | Chervov, A. | |
| dc.creator | Rybnikov, L. | |
| dc.date | 2004-09-01 | |
| dc.date.accessioned | 2026-07-07T04:17:23Z | |
| dc.date.available | 2026-07-07T04:17:23Z | |
| dc.description | We propose the following receipt to obtain the quantization of the Poisson submanifold $N$ defined by the equations $f_i=0$ (where $f_i$ are Casimirs) from the known quantization of the manifold $M$: one should consider factor algebra of the quantized functions on $M$ by the images of $D(f_i)$, where $D: Fun(M) \to Fun(M)\otimes \CC[\hbar]$ is Duflo-Kirillov-Kontsevich map. We conjecture that this algebra is isomorphic to quantization of $Fun(N)$ with Poisson structure inherited from $M$. Analogous conjecture concerning the Hamiltonian reduction saying that "deformation quantization commutes with reduction" is presented. The conjectures are checked in the case of $S^2$ which can be quantized as a submanifold, as a reduction and using recently found explicit star product. It's shown that all the constructions coincide. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/0409005 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0409005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52733 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Algebra | |
| dc.title | Deformation quantization of submanifolds and reductions via Duflo-Kirillov-Kontsevich map | |
| dc.type | text |