On Self-Adjointness of 3D - Dirac Operators with Singular Potentials

We consider the Dirac operator on ℝ3, DA,Φ , Qs = ∑ j=13 αj (i∂ xj + Aj (x)) + α 0m - Φ (x)I4 + Qs, with magnetic potential A (x) = (A 1(x), A 2(x), A 3(x))) and electrostatic potential Φ(x), where αj,j = 0, 1, 2, 3 are the Dirac matrices, Qs = ΓδS is a singular potential where δS is the Dirac δ - function with support on an enough smooth surface S ⊂ 3 divided 3 on two open domains Ω+, Ω- with common unbounded boundary S, and Γ is 4 × 4 matrix. We associate with the formal Dirac operator D A, Φ, Qs the unbounded in the Hilbert space L 2(3, 4) operator D with domain defined by some interaction conditions on the surface S. The purpose of the paper is to give conditions of the self-adjointness of the operator D.