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arXiv · 2412.17396

Local Boundary Conditions for Dirac-type operators

Nadine Große·Alejandro Uribe·Hanne van den Bosch
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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 $3$ and $4$. With the same techniques we can also treat transmission boundary conditions.

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Nadine Große, Alejandro Uribe, Hanne van den Bosch. 2024-12-23. Local Boundary Conditions for Dirac-type operators. https://arxiv.org/abs/2412.17396

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