Boundary Value Problems for Dirac Operators on Graphs - Richtsfeld, Alberto (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
We carry the index theory for manifolds with boundary of Bär and Ballmann over to first-order differential operators on metric graphs. This approach yields a short proof of the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle are studied. We also introduce two types of boundary conditions for the Dirac operator, whose spectra encode information about the underlying graph topology.