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Scattering of particles by long-range magnetic fields. (English) Zbl 0646.35074

The scattering of nonrelativistic particles (either quantum mechanical or classical) by a magnetic field B is studied in any dimension \(\nu\geq 2\). \(B(x)\) is allowed to decay like \(| x|^{-3/2-\delta}\) \((\delta >0)\), as \(| x| \to \infty\). Assumptions are made about the field strengths and not about the potentials. A gauge is constructed for which the unmodified wave operators exist and are complete even though the corresponding classical motion need not be asymptotically free. The result also holds for Yang-Mills fields.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81U99 Quantum scattering theory
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