Non-commutative Bloch theory

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dc.creatorGruber, Michael J.
dc.date2000-06-24
dc.date.accessioned2026-07-07T04:27:51Z
dc.date.available2026-07-07T04:27:51Z
dc.descriptionFor differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a non-commutative Bloch theory for elliptic operators on Hilbert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies e.g. to differential operators invariant under a projective group action, such as Schroedinger, Dirac and Pauli operators with periodic magnetic field, as well as to discrete models, such as the almost Matthieu equation and the quantum pendulum.
dc.description37 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0006021
dc.identifierhttp://arxiv.org/abs/math-ph/0006021
dc.identifierJ. Math. Phys. 42.6 (2001), 2438-2465
dc.identifierdoi:10.1063/1.1369122
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56573
dc.subjectMathematical Physics
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subjectQuantum Physics
dc.subject46L89; 35Q40, 58C40, 58G25
dc.titleNon-commutative Bloch theory
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