Journal of Operator Theory

Volume 46, Issue 2, Fall 2001 pp. 289-321.

On the spectral theory of singular Dirac type hamiltonians

Authors: V. Georgescu (1), and M. Mantoiu (2)
Author institution: (1) Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
(2) Institute of Mathematics, Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania

Summary: We introduce a class of matrix valued pseudo-differential operators that admit scalar locally conjugate operators $\textrm{(in the sense of E. Mourre)}$ and we give a general method of study of singular perturbations of such operators. In particular, we develop the spectral and scattering theory for a class of hamiltonians which contains the Dirac operators with arbitrary Coulomb singularities.

Keywords: Dirac operator, singular perturbation, Mourre estimate, limiting absorption principle, wave operators

Contents Full-Text PDF