2003/12/13 by Shamgar Gurevich, Ronny Hadani, Gurevich, Shamgar +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Representation Theory (math.RT) #math-ph #math.MP #math.RT #quant-ph
paper · pdf · doi:10.48550/arxiv.math-ph/0312039
11 pages
openalex publication_date 2003/12/13 · arxiv created 2005/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 = SL2 (\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 ∈ \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.