{
  "id": "1402.4949",
  "version": "v2",
  "published": "2014-02-20T10:21:52.000Z",
  "updated": "2014-10-28T14:30:54.000Z",
  "title": "The renormalisation group via statistical inference",
  "authors": [
    "Cédric Bény",
    "Tobias J. Osborne"
  ],
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalisation group arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and identifies the role played by information in renormalisation. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalisation techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-20T10:21:52.000Z",
      "abstract": "In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of theories. Here it is argued that the renormalisation group arises from the inherent ambiguities in constructing the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives of the equivalence classes. This provides a unifying framework and identifies the role played by information in renormalisation. We validate this idea by showing that it justifies the use of low-momenta n-point functions as relevant observables around a gaussian hypothesis. Our methods also provide a way to extend renormalisation techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the distinctions between various type of RG.",
      "comment": "This is a digest of arXiv:1310.3188",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-28T14:30:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "statistical inference",
      "renormalisation group arises",
      "encounters flow parameters",
      "low-momenta n-point functions",
      "extend renormalisation techniques"
    ],
    "publication": {
      "doi": "10.1088/1367-2630/17/8/083005",
      "journal": "New Journal of Physics",
      "year": 2015,
      "month": "Aug",
      "volume": 17,
      "number": 8,
      "pages": "083005"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1282052,
      "adsabs": "2015NJPh...17h3005B"
    }
  }
}