{
  "id": "1903.09621",
  "version": "v1",
  "published": "2019-03-20T06:35:53.000Z",
  "updated": "2019-03-20T06:35:53.000Z",
  "title": "Random fields, large deviations and triviality in quantum field theory. Part I",
  "authors": [
    "Adnan Aboulalaa"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the field $\\phi_{d}^{4}$ is obtained as a limit of regularized fields $\\phi_{d, k}^{4}$ associated with a probability measures $\\mu_{k,V}$, where $k, V$ represent an ultraviolet and volume cutoffs. The result obtained is the following alternative: (1) either the renormalized field $\\phi_{4}^{4}$ is the trivial free field, or (2) the almost sure limit of the density of $\\mu_{k,V}$, with respect to the Gaussian free field measure, exists and is equal to $0$. This implies, in the second case, that $\\mu_{k,V}$ can not have a strong limit as $k \\longrightarrow \\infty$. These assertions are valid in finite volume. They also hold for vector fields and can be extended to polynomial Lagrangians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-20T06:35:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60F10",
      "60K35",
      "81T08",
      "81T16"
    ],
    "keywords": [
      "quantum field theory",
      "random fields",
      "triviality",
      "euclidean quantum scalar field",
      "gaussian free field measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}