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      Gauge Transformations and Inverse Quantum Scattering with Medium-Range Magnetic Fields

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          Abstract

          The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are considered. The electrostatic potential A_0 shall be short-range, and the magnetic field B shall decay faster than |x|^{-3/2} . A natural class of corresponding vector potentials A of medium range is introduced, and the decay and regularity properties of various gauges are discussed, including the transversal gauge, the Coulomb gauge, and the Griesinger vector potentials. By a suitable combination of these gauges, B need not be differentiable. The scattering operator S is not invariant under the corresponding gauge transformations, but experiences an explicit transformation. Both B and A_0 are reconstructed from an X-ray transform, which is obtained from the high-energy limit of S . Here previous results by Arians and Nicoleau are generalized to the medium-range situation. In a sequel paper, medium-range vector potentials are applied to relativistic scattering.

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          Proof of the charge superselection rule in local relativistic quantum field theory

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            The Aharonov-Bohm effect and scattering theory

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              On the equations rot v=g and div u=f with zero boundary conditions

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                Author and article information

                Journal
                2004-12-30
                2005-07-14
                Article
                math-ph/0412096
                fe68dce1-feb5-4346-a711-b78f05c2ab09
                History
                Custom metadata
                81U40
                MPEJ vol 11, No 5, December 2005, 32 pp.
                30+2 pages, updated with minor changes, new appendix contains a preview of the sequel paper
                math-ph math.MP

                Mathematical physics,Mathematical & Computational physics
                Mathematical physics, Mathematical & Computational physics

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