Hamiltonian self-adjoint extensions for (2+1)-dimensional Dirac particles

We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux phi = 2 pi kappa /e. The rotational invariance of this configuration implies that the subspaces of definite angular momentum l + 1/2 are invariant under the action of the Hamiltonian H. We show that for kappa - l greater than or equal to 1 or kappa - 1 less than or equal to 0 the restriction of H to these subspaces, Hr, is essentially self-adjoint, while for 0 < kappa - l < 1 H-l admits a one-parameter family of self-adjoint extensions (SAEs). In the latter case, the functions in the domain of H-l are singular (but square integrable) at the origin, their behaviour being dictated by the value of the parameter gamma that identifies the SAE. We also determine the spectrum of the Hamiltonian as a function of kappa and gamma, as well as its closure.