  By using the spherical coordinates in 3+1 dimensions we study the
self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an
infinitely thin magnetic flux tube. It is shown that the angular part of the
Dirac Hamiltonian requires self-adjoint extensions as well as its radial one.
The self-adjoint extensions of the angular part are parametrized by 2x2 unitary
matrix.
