Abstract
We study relativistic scattering theory for the Dirac equation in the presence of a long-range magnetic field B( x) ~ const. (1 + ¦x¦) −3 2 − δ . Making use of the gauge freedom we prove asymptotic completeness for the unmodified Møller operators, although the vector potential decays very slowly. This generalizes a corresponding nonrelativistic result in [5]. The main new problem is to control the effects of “Zitterbewegung”. Our proof also works for Yang-Mills fields.
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