Asymptotics near +-m of the spectral shift function for Dirac operators with non-constant magnetic fields

Details Asymptotics near +-m of the spectral shift function for Dirac operators with non-constant magnetic fields Asymptotics near +-m of the spectral shift function for Dirac operators with non-constant magnetic fields

2009-11-13

arxiv.org/abs/0911.2616v1

Physics

Mathematical Physics

26 pages

Scientific paper

We consider a 3-dimensional Dirac operator H_0 with non-constant magnetic field of constant direction, perturbed by a sign-definite matrix-valued potential V decaying fast enough at infinity. Then we determine asymptotics, as the energy goes to +m and -m, of the spectral shift function for the pair (H_0,H_0+V). We obtain, as a by-product, a generalised version of Levinson's Theorem relating the eigenvalues asymptotics of H_0+V near +m and -m to the scattering phase shift for the pair (H_0,H_0+V).

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