Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17396 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916828122447872 |
|---|---|
| author | Große, Nadine Uribe, Alejandro Bosch, Hanne van den |
| author_facet | Große, Nadine Uribe, Alejandro Bosch, Hanne van den |
| contents | We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value problems for Dirac operators as in [BB12] and pointwise considerations, for local smooth boundary conditions the question of being self-adjoint resp. regular is fully translated into linear-algebraic language at each boundary point. We analyse these conditions and classify them in low dimensions and ranks. In particular, we classify all local self-adjoint regular boundary conditions for Dirac spinors (four spinor components) in dimensions $3$ and $4$. With the same techniques we can also treat transmission boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Boundary Conditions for Dirac-type operators Große, Nadine Uribe, Alejandro Bosch, Hanne van den Mathematical Physics Differential Geometry We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value problems for Dirac operators as in [BB12] and pointwise considerations, for local smooth boundary conditions the question of being self-adjoint resp. regular is fully translated into linear-algebraic language at each boundary point. We analyse these conditions and classify them in low dimensions and ranks. In particular, we classify all local self-adjoint regular boundary conditions for Dirac spinors (four spinor components) in dimensions $3$ and $4$. With the same techniques we can also treat transmission boundary conditions. |
| title | Local Boundary Conditions for Dirac-type operators |
| topic | Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2412.17396 |