The Two Dimensional Hannay-Berry Model

dc.creatorGurevich, Shamgar
dc.creatorHadani, Ronny
dc.date2003-12-13
dc.date2005-10-21
dc.date.accessioned2026-07-07T06:35:19Z
dc.date.available2026-07-07T06:35:19Z
dc.descriptionThe 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.description11 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0312039
dc.identifierhttp://arxiv.org/abs/math-ph/0312039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99760
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.subjectQuantum Physics
dc.titleThe Two Dimensional Hannay-Berry Model
dc.typetext

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