Local Boundary Conditions for Dirac-type operators
Abstract
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 and . With the same techniques we can also treat transmission boundary conditions.
Keywords
Cite
@article{arxiv.2412.17396,
title = {Local Boundary Conditions for Dirac-type operators},
author = {Nadine Große and Alejandro Uribe and Hanne van den Bosch},
journal= {arXiv preprint arXiv:2412.17396},
year = {2025}
}
Comments
The section on transmission conditions was revised and the references were updated