{
  "id": "1209.2148",
  "version": "v3",
  "published": "2012-09-10T20:24:34.000Z",
  "updated": "2017-11-12T17:28:32.000Z",
  "title": "Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields",
  "authors": [
    "Romeo Brunetti",
    "Klaus Fredenhagen",
    "Pedro Lauridsen Ribeiro"
  ],
  "comment": "58 pages, no figures. Version 3: radical changes in Sec.3.2 for the part on Peierls' bracket and related results, added citations and acknowledgements",
  "categories": [
    "math-ph",
    "hep-th",
    "math.AP",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and functorial, being characterized by a combination of geometric, analytic and algebraic elements which (1) make it closer to quantum field theory, (2) allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and (3) provide a new pathway towards understanding dynamics. Particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and the functorial structure underlying our approach.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-18T15:17:27.000Z",
      "title": "Algebraic Structure of Classical Field Theory I: Kinematics and Linearized Dynamics for Real Scalar Fields",
      "comment": "53 pages, no figures. Version 2: corrected a mistake in the proof of Corollary 4.0.19, minor rewording, added remark and acknowledgement",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-11-12T17:28:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70S05",
      "70S20",
      "17B63",
      "35L10",
      "35L72",
      "58C15"
    ],
    "keywords": [
      "classical field theory",
      "real scalar fields",
      "algebraic structure",
      "algebraic quantum field theory",
      "linearized dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1185123,
      "adsabs": "2012arXiv1209.2148B"
    }
  }
}