Abstract
We 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 ±m. In particular, it is shown that the operator \((1 + \left| x \right|^2 )^{ - 1/2}\)-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 \(H = H_0 + V\).
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Iftimovici, A., Măntoiu, M. Limiting Absorption Principle at Critical Values for the Dirac Operator. Letters in Mathematical Physics 49, 235–243 (1999). https://doi.org/10.1023/A:1007625918845
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DOI: https://doi.org/10.1023/A:1007625918845