The Two Dimensional Hannay-Berry Model
Gurevich, Shamgar ; Hadani, Ronny
arXiv, 0312039 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-12-13
Classification:  Mathematical Physics,  Mathematics - Representation Theory,  Quantum Physics 
@article{0312039,
     author = {Gurevich, Shamgar and Hadani, Ronny},
     title = {The Two Dimensional Hannay-Berry Model},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312039}
}

Gurevich, Shamgar; Hadani, Ronny. The Two Dimensional Hannay-Berry Model. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312039/