Local Boundary Conditions for Dirac-type operators
Abstrak
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.
Penulis (3)
Nadine Große
Alejandro Uribe
Hanne van den Bosch
Akses Cepat
- Tahun Terbit
- 2024
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓