{
  "id": "1508.04655",
  "version": "v1",
  "published": "2015-08-19T14:20:30.000Z",
  "updated": "2015-08-19T14:20:30.000Z",
  "title": "Continuity of Scalar Fields With Logarithmic Correlations",
  "authors": [
    "S. G. Rajeev",
    "Evan Ranken"
  ],
  "comment": "14 pages, 4 figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We apply select ideas from the modern theory of stochastic processes in order to study the continuity/roughness of scalar quantum fields. A scalar field with logarithmic correlations (such as a massless field in 1+1 spacetime dimensions) has the mildest of singularities, making it a logical starting point. Instead of the usual inner product of the field with a smooth function, we introduce a moving average on an interval which allows us to obtain explicit results and has a simple physical interpretation. Using the mathematical work of Dudley, we prove that the averaged random process is in fact continuous, and give a precise modulus of continuity bounding the short-distance variation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-19T14:20:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmic correlations",
      "scalar field",
      "continuity",
      "scalar quantum fields",
      "usual inner product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}