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On the spectral theory of singular Dirac type Hamiltonians. (English) Zbl 0993.35070

Summary: We introduce a class of matrix valued pseudo-differential operators that admit scalar locally conjugate operators (in the sense of E. Mourre) and give a general method for the 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.

MSC:

35P05 General topics in linear spectral theory for PDEs
47F05 General theory of partial differential operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35B25 Singular perturbations in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
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