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

We study the stationary problem of a charged Dirac particle in (2+1) dimens ions 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 configu ration 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 restri ction 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 extensio ns (SAEs). In the latter case, the functions in the domain of H-l are singu lar (but square integrable) at the origin, their behaviour being dictated b y the value of the parameter gamma that identifies the SAE. We also determi ne the spectrum of the Hamiltonian as a function of kappa and gamma, as wel l as its closure.