Geometric Quantization and No Go Theorems
| dc.creator | Ginzburg, Viktor L. | |
| dc.creator | Montgomery, Richard | |
| dc.date | 1997-03-18 | |
| dc.date.accessioned | 2026-07-07T09:13:01Z | |
| dc.date.available | 2026-07-07T09:13:01Z | |
| dc.description | A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a consequence of a ``no go'' theorem claiming that the entire Lie algebra of smooth functions on a compact symplectic manifold cannot be quantized, i.e., it has no essentially nontrivial finite-dimensional representations. | |
| dc.description | AMS-LaTeX, 10 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9703010 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9703010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152220 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53F05 (Primary) 58F06, 81S10 (Secondary) | |
| dc.title | Geometric Quantization and No Go Theorems | |
| dc.type | text |