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 a 2 × 2 unitary matrix. ∗e-m...

The purpose of this note is to present several criteria for essential self– adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert spa...

We study the essential self-adjointness for real principal type differential operators. Unlike elliptic case, we need geometric conditions even operators on Euclidean space with asymptotically constant coefficients, and prove under null non-trapping condition.