The free Dirac operator on compact and noncompact graphs

The free Dirac operator defined on composite one-dimensional structures consisting of finitely many half-lines and intervals is investigated. The influence of the connection points between the constituents is modeled by transition conditions for the wave functions or equivalently by different self-adjoint extensions of the Dirac operator. General relations between the parameters of the extensions and the eigenvalues resp. the scattering coefficients are derived and then applied to the cases of a bundle of half-lines, a point defect, a branching line, and an eye-shaped structure.