Absolutely continuous spectrum of Dirac operators for long-range potentials

AbstractUsing the resolvent method and the technique of weighted L2-estimates we deduce the non-existence of the singular continuous spectrum of the Dirac operator τ + P(x) on the interval (1, ∞). We assume that the hermitian matrix potential P(x) = P1(x) + P2(x) is divided into a long-range part P1(x) = O(¦x¦−ε), [r ∂rP1(x)]− = O(¦x¦−ε) and a short-range part P2(x) = O(¦x¦−1 − ε) (¦x¦ → ∞) with local singularities P(x) = O(¦x − aj¦−1) of Coulomb type for N nuclei a1,…,aN∈R3