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

Rafael Tiedra de Aldecoa (1)

1 UC - Pontificia Universidad Católica de Chile

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).

Mots clés: spectral shift function; Dirac operator; magnetic field; critical values

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rafael Tiedra de Aldecoa. Asymptotics near +-m of the spectral shift function for Dirac operators with non-constant magnetic fields. 2009. ⟨hal-00431895⟩