The geometry emerging from the symmetries of a quantum system

dc.contributor.areaMathematicsen_US
dc.contributor.authorDe Nittis, Giuseppeen_US
dc.contributor.authorPanati, Gianlucaen_US
dc.contributor.departmentMathematical Physicsen_US
dc.date.accessioned2010-01-26T16:38:35Zen_US
dc.date.accessioned2011-09-07T20:19:53Z
dc.date.available2010-01-26T16:38:35Zen_US
dc.date.available2011-09-07T20:19:53Z
dc.date.issued2010-01-26T16:38:35Zen_US
dc.description.abstractWe 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.extent578198 bytesen_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/3834en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesSISSA;72/2009/FMen_US
dc.relation.ispartofseriesarXiv.org;0911.5270en_US
dc.titleThe geometry emerging from the symmetries of a quantum systemen_US
dc.typePreprinten_US
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