Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00173583" target="_blank" >RIV/68407700:21340/11:00173583 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.geomphys.2010.12.004" target="_blank" >http://dx.doi.org/10.1016/j.geomphys.2010.12.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2010.12.004" target="_blank" >10.1016/j.geomphys.2010.12.004</a>

Result language
angličtina
Original language name
Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields
Original language description
Given an invariant gauge potential and a periodic scalar potential on a Riemannian manifold M with a discrete symmetry group, we consider a periodic quantum Hamiltonian H constructed as a sum of the Bochner Laplacian and the potential. Both the gauge group and the symmetry group can be noncommutative, and the gauge field need not vanish. With any unitary representation L of the symmetry group one associates a Hamiltonian H_L on the factor manifold. We describe a construction of the Bloch decomposition of the periodic Hamiltonian H into a direct integral over the dual space to the symmetry group whose components are H_L. Conversely, given a fixed representation L of the symmetry group, one can express the propagator associated with H_L on the factor manifold in terms of the propagator associated with the periodic Hamiltonian H. Furthermore, we show that these constructions are mutually inverse.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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