{
  "id": "1207.2751",
  "version": "v2",
  "published": "2012-07-11T19:31:27.000Z",
  "updated": "2013-03-28T16:23:59.000Z",
  "title": "A Rigorous Path Integral for N=1 Supersymmetic Quantum Mechanics on a Riemannian Manifold",
  "authors": [
    "Dana Fine",
    "Stephen Sawin"
  ],
  "comment": "Minor changes in introduction, exposition and title based on referees' comments",
  "categories": [
    "math-ph",
    "hep-th",
    "math.DG",
    "math.MP"
  ],
  "abstract": "Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-Beltrami operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-28T16:23:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q60",
      "81Q35",
      "53Z05",
      "58J20"
    ],
    "keywords": [
      "supersymmetic quantum mechanics",
      "rigorous path integral",
      "heat kernel",
      "steepest descent approximation",
      "supersymmetric quantum mechanics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1122058,
      "adsabs": "2012arXiv1207.2751F"
    }
  }
}