{
  "id": "hep-ph/9905239",
  "version": "v2",
  "published": "1999-05-04T14:17:46.000Z",
  "updated": "1999-08-02T11:28:58.000Z",
  "title": "From hard thermal loops to Langevin dynamics",
  "authors": [
    "Dietrich Bodeker"
  ],
  "comment": "42 pages, 2 figures, uses elsart.sty; explanatory paragraph added to the introduction, 4 references added, a few quotations added; to appear in Nucl. Phys. B",
  "journal": "Nucl.Phys.B559:502-538,1999",
  "doi": "10.1016/S0550-3213(99)00435-6",
  "categories": [
    "hep-ph",
    "hep-lat",
    "hep-th",
    "nucl-th"
  ],
  "abstract": "In hot non-Abelian gauge theories, processes characterized by the momentum scale $g^2 T$ (such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft ($|\\vec{p}|\\sim g^2 T$) field modes is obtained by integrating out momenta larger than $g^2 T$. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale $T$, it is shown how to integrate out the scale $gT$ in an expansion in the gauge coupling $g$. At leading order in $g$, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as $\\Gamma = \\kappa g^{10} \\log(1/g) T^4$, and it allows for a calculation of $\\kappa$ on the lattice.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-08-02T11:28:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.10.Wx",
      "11.15.Kc",
      "11.30.Fs"
    ],
    "keywords": [
      "langevin dynamics",
      "soft field modes",
      "hot baryon number violation rate",
      "hard thermal loop effective theory",
      "collision term"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Nucl. Phys. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 499302
    }
  }
}