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

2009/11/13 by Rafael Tiedra De Aldecoa, De Aldecoa, Rafael Tiedra
Mathematics · Physics and Astronomy · #35P20 #35P25 #35Q41 #47F05 #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35P20 #msc:35P25 #msc:35Q41 #msc:47F05 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.0911.2616

26 pages

arxiv created 2009/11/13 · arxiv updated 2009/12/01

Abstract

We consider a 3-dimensional Dirac operator H₀ 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 (H₀,H₀+V). We obtain, as a by-product, a generalised version of Levinson's Theorem relating the eigenvalues asymptotics of H₀+V near +m and -m to the scattering phase shift for the pair (H₀,H₀+V).

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