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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | 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 |
| Цитувати: | Boundary Value Problems for Dirac Operators on Graphs. Alberto Richtsfeld. SIGMA 20 (2024), 022, 23 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |