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The geometry emerging from the symmetries of a quantum system

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dc.contributor.author De Nittis, Giuseppe en_US
dc.contributor.author Panati, Gianluca en_US
dc.date.accessioned 2010-01-26T16:38:35Z en_US
dc.date.accessioned 2011-09-07T20:19:53Z
dc.date.available 2010-01-26T16:38:35Z en_US
dc.date.available 2011-09-07T20:19:53Z
dc.date.issued 2010-01-26T16:38:35Z en_US
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/3834 en_US
dc.description.abstract We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of "continuous sections" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne's thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result. en_US
dc.format.extent 578198 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;72/2009/FM en_US
dc.relation.ispartofseries arXiv.org;0911.5270 en_US
dc.title The geometry emerging from the symmetries of a quantum system en_US
dc.type Preprint en_US
dc.contributor.department Mathematical Physics en_US
dc.contributor.area Mathematics en_US


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