Self-adjointness of the 2D Dirac Operator with Singular Interactions Supported on Star Graphs

We consider the two-dimensional Dirac operator with Lorentz-scalar \(\delta \)-shell interactions on each edge of a star graph. An orthogonal decomposition is performed which shows such an unitarily equivalent to sum half-line operators off-diagonal Coulomb potentials. This reduces computation deficiency indices determining number eigenvalues one-dimensional spin–orbit in interval \((-1/2,1/2)\). If edges graph two or three, these can then be analytically determined for range parameters. For higher numbers edges, it possible numerically calculate indices. Among others, examples are given where strength directly change indices, while other parameters all fixed and (2, 2), neither have been observed literature best knowledge authors. those not already self-adjoint do 0 spectrum associated operator, distinguished extension also characterized.