{
  "id": "1611.08538",
  "version": "v1",
  "published": "2016-11-25T18:03:21.000Z",
  "updated": "2016-11-25T18:03:21.000Z",
  "title": "Mass Renormlization in the Nelson Model",
  "authors": [
    "Fumio Hiroshima",
    "Susumu Osawa"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The asymptotic behavior of the effective mass $m_{\\rm eff}(\\Lambda)$ of the so-called Nelson model in quantum field theory is considered, where $\\Lambda$ is an ultraviolet cutoff parameter of the model. Let $m$ be the bare mass of the model. It is shown that for sufficiently small coupling constant $|\\alpha|$ of the model, $m_{{\\rm eff}}(\\Lambda)/m$ can be expanded as $m_{{\\rm eff}}(\\Lambda)/m= 1+\\sum_{n=1}^\\infty a_n(\\Lambda) \\alpha^{2n}$. A physical folklore is that $a_n(\\Lambda)\\sim [\\log \\Lambda]^{(n-1)}$ as $\\Lambda\\to \\infty$. It is rigorously shown that $$0<\\lim_{\\Lambda\\to\\infty}a_1(\\Lambda)<C,\\quad C_1\\leq \\lim_{\\Lambda\\to\\infty}a_2(\\Lambda)/\\log\\Lambda\\leq C_2$$ with some constants $C$, $C_1$ and $C_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-25T18:03:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nelson model",
      "mass renormlization",
      "quantum field theory",
      "ultraviolet cutoff parameter",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}