Limiting absorption principle at critical values for the Dirac operator (Q1971968)

The authors prove estimates for the resolvent \((H_0- z)^{-1}\) of the Dirac operator \(H_0= \alpha\cdot P+ m\beta\), valid even for \(z\) close to the critical points \(\pm m\). In particular, it is shown that the operator \((1+|x|^2)^{-1/2}\) is globally \(H_0\)-smooth. As a by-product, the absence of the singular spectrum as well as the existence and unitarity of the wave operators are obtained for a class of perturbations \(H= H_0+ V\).