{
  "id": "quant-ph/0003107",
  "version": "v1",
  "published": "2000-03-22T18:41:42.000Z",
  "updated": "2000-03-22T18:41:42.000Z",
  "title": "Gauss Sums and Quantum Mechanics",
  "authors": [
    "Vernon Armitage",
    "Alice Rogers"
  ],
  "comment": "14 pages, LaTeX",
  "doi": "10.1088/0305-4470/33/34/305",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "math.NT"
  ],
  "abstract": "By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-22T18:41:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanics",
      "phase space",
      "finite sums",
      "quadratic gauss sums",
      "paths method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}