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 |
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| Datum: | 2024 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| 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.
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| ISSN: | 1815-0659 |