Quantum Numbers of the Theta Vacuum in (2+1)-Dimensional Spinor   Electrodynamics: Charge and Magnetic Flux
  A singular configuration of an external static vector field in the form of a magnetic string polarizes the vacuum of a second-quantized theory on the plane orthogonal to the string axis. The most general boundary conditions at the punctured singular point that are compatible with the self-adjointness of two-dimensional Dirac Hamiltonian are considered. The dependences of the induced vacuum quantum numbers on the parameter of the self-adjoint extension, on the string flux, and on the choice of irreducible representation of the matrices in (2+1)-dimensional spacetime are disscussed. 
Yu. A. Sitenko and D. G. Rakityansky