Boundary Value Problems for Dirac Operators on Graphs

We carry the index theory for manifolds with boundary of Bär and Ballmann over to first-order differential operators on metric graphs. This approach yields a short proof of the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2024
1. Verfasser: Richtsfeld, Alberto
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212173
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Boundary Value Problems for Dirac Operators on Graphs. Alberto Richtsfeld. SIGMA 20 (2024), 022, 23 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:We carry the index theory for manifolds with boundary of Bär and Ballmann over to first-order differential operators on metric graphs. This approach yields a short proof of the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle are studied. We also introduce two types of boundary conditions for the Dirac operator, whose spectra encode information about the underlying graph topology.
ISSN:1815-0659