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<p>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 [<CitationRef CitationID="CR4">4</CitationRef>] 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 analyze 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.</p>

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Local Boundary Conditions for Dirac-Type Operators

  • 期刊论文

  • 发表日期：

    2025年10月17日

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  • N. Grosse,
  • A. Uribe,
  • H. Van Den Bosch

摘要

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 [4] 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 analyze 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.