{
  "id": "math-ph/0412096",
  "version": "v2",
  "published": "2004-12-30T22:41:38.000Z",
  "updated": "2005-07-14T13:40:33.000Z",
  "title": "Gauge Transformations and Inverse Quantum Scattering with Medium-Range Magnetic Fields",
  "authors": [
    "Wolf Jung"
  ],
  "comment": "30+2 pages, updated with minor changes, new appendix contains a preview of the sequel paper",
  "journal": "MPEJ vol 11, No 5, December 2005, 32 pp.",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-14T13:40:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81U40"
    ],
    "keywords": [
      "medium-range magnetic fields",
      "gauge transformations",
      "inverse quantum scattering",
      "high-energy limit",
      "medium-range vector potentials"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.ph..12096J"
    }
  }
}