Abstract:
We construct and classify self-adjoint realisations of the Dirac operator on
a compact, metric graph and discuss circumstances under which chiral symmetry is
realised. We then establish some spectral properties. Extending the quantum graph models
to include a time variable, we introduce a coupling to abelian gauge fields. In these
extended models we establish self-adjointness and chiral symmetry, and discuss some spectral
properties. We finally approach an index theorem that serves as an important input for a
Schwinger model on a graph.
