The Two Dimensional Hannay-Berry Model
| dc.creator | Gurevich, Shamgar | |
| dc.creator | Hadani, Ronny | |
| dc.date | 2003-12-13 | |
| dc.date | 2005-10-21 | |
| dc.date.accessioned | 2026-07-07T06:35:19Z | |
| dc.date.available | 2026-07-07T06:35:19Z | |
| dc.description | The main goal of this paper is to construct the Hannay-Berry model of quantum mechanics, on a two dimensional symplectic torus. We construct a simultaneous quantization of the algebra of functions and the linear symplectic group $\G =$ SL$_2 (\Z)$. We obtain the quantization via an action of $\G$ on the set of equivalence classes of irreducible representations of Rieffel`s quantum torus $\Ad$. For $\h \in \Q$ this action has a unique fixed point. This gives a canonical projective equivariant quantization. There exists a Hilbert space on which both $\G$ and $\Ad$ act equivariantly. Combined with the fact that every projective representation of $\G$ can be lifted to a linear representation, we also obtain linear equivariant quantization. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0312039 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0312039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99760 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Physics | |
| dc.title | The Two Dimensional Hannay-Berry Model | |
| dc.type | text |