{
  "id": "1805.08795",
  "version": "v1",
  "published": "2018-05-22T18:00:20.000Z",
  "updated": "2018-05-22T18:00:20.000Z",
  "title": "Homotopy theory of algebraic quantum field theories",
  "authors": [
    "Marco Benini",
    "Alexander Schenkel",
    "Lukas Woike"
  ],
  "comment": "34 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.AT",
    "math.MP"
  ],
  "abstract": "Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical model structure and explain the important conceptual and also practical consequences of this result. As a concrete application we provide a derived version of Fredenhagen's universal algebra construction, which is relevant e.g. for the BRST/BV formalism. We further develop a homotopy theoretical generalization of algebraic quantum field theory with a particular focus on the homotopy-coherent Einstein causality axiom. We provide examples of such homotopy-coherent theories via (1) smooth normalized cochain algebras on $\\infty$-stacks, and (2) fiber-wise groupoid cohomology of a category fibered in groupoids with coefficients in a strict quantum field theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-22T18:00:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Txx",
      "18D50",
      "18G55",
      "55U35"
    ],
    "keywords": [
      "algebraic quantum field theory",
      "homotopy theory",
      "chain complex valued algebraic quantum",
      "complex valued algebraic quantum field",
      "fredenhagens universal algebra construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}