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 [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. © Springer Nature Switzerland AG 2025.