{
  "id": "math-ph/9910036",
  "version": "v2",
  "published": "1999-10-22T18:47:16.000Z",
  "updated": "1999-10-27T14:40:25.000Z",
  "title": "The analytic quantum information manifold",
  "authors": [
    "R. F. Streater"
  ],
  "comment": "12 pages LATEX; to appear in \"Stochastic processes, physics and geometry: new interplays\"; eds. F. Gesztesy, S. Paycha and H. Holden. Canad. Math. Soc. In this replacement, I have made clear that it is the partition function that possesses a convergent power series with the given radius of convergence. The free-energy is real analytic only in an unspecified hood of the real axis",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "Let H be a self-adjoint operator such that exp(-aH) is of trace class for some a<1. Let V be a symmetric operator, Kato bounded relative to H. We show that log Tr[exp(-H+xV)] is a real analytic function of x in a hood of x=0. We show that the Gibbs states of H+xV form a real analytic Banach manifold. This work has been extended in math-ph/9910031.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-10-27T14:40:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58B20",
      "53C80"
    ],
    "keywords": [
      "analytic quantum information manifold",
      "real analytic banach manifold",
      "real analytic function",
      "trace class",
      "gibbs states"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.ph..10036S"
    }
  }
}