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...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| ISSN: | 1815-0659 |
| 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| _version_ | 1862618702586839040 |
|---|---|
| author | Richtsfeld, Alberto |
| author_facet | Richtsfeld, Alberto |
| citation_txt | Boundary Value Problems for Dirac Operators on Graphs. Alberto Richtsfeld. SIGMA 20 (2024), 022, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-14T11:10:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212173 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T11:10:01Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Richtsfeld, Alberto 2026-01-30T08:18:53Z 2024 Boundary Value Problems for Dirac Operators on Graphs. Alberto Richtsfeld. SIGMA 20 (2024), 022, 23 pages 1815-0659 2020 Mathematics Subject Classification: 34B45; 58J50 arXiv:2307.13324 https://nasplib.isofts.kiev.ua/handle/123456789/212173 https://doi.org/10.3842/SIGMA.2024.022 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. I would like to thank Christian Bär, Lashi Bandara, and Klaus Ecker for their supervision and for making this project possible. I would also like to thank the anonymous referees for their helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Boundary Value Problems for Dirac Operators on Graphs Article published earlier |
| spellingShingle | Boundary Value Problems for Dirac Operators on Graphs Richtsfeld, Alberto |
| title | Boundary Value Problems for Dirac Operators on Graphs |
| title_full | Boundary Value Problems for Dirac Operators on Graphs |
| title_fullStr | Boundary Value Problems for Dirac Operators on Graphs |
| title_full_unstemmed | Boundary Value Problems for Dirac Operators on Graphs |
| title_short | Boundary Value Problems for Dirac Operators on Graphs |
| title_sort | boundary value problems for dirac operators on graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212173 |
| work_keys_str_mv | AT richtsfeldalberto boundaryvalueproblemsfordiracoperatorsongraphs |