{
  "id": "1805.10317",
  "version": "v1",
  "published": "2018-05-25T18:27:39.000Z",
  "updated": "2018-05-25T18:27:39.000Z",
  "title": "Lagrangian field theories: ind/pro-approach and L-infinity algebra of local observables",
  "authors": [
    "Nestor Leon Delgado"
  ],
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP",
    "math.SG"
  ],
  "abstract": "Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to different topological and Frech\\'et structures on it. A category of local (insular) manifolds has been constructed. Noether's second theorem is reviewed and the notion of Lie pseudogroups is explored using these concepts. The L-infinity algebra of local observables is defined depending only on the cohomology of the Lagrangian (using a result in multisymplectic manifold which has been extended to the local category). That local pre-multisymplectic form, called the Poincar\\'e-Cartan can be thought of as a coordinate free, cohomological version of other similar structures in the field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T18:27:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D05"
    ],
    "keywords": [
      "lagrangian field theories",
      "local observables",
      "l-infinity algebra",
      "ind/pro-approach",
      "pro-finite dimensional smooth manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}