{
  "id": "1603.09626",
  "version": "v1",
  "published": "2016-03-31T15:07:51.000Z",
  "updated": "2016-03-31T15:07:51.000Z",
  "title": "Fedosov Quantization and Perturbative Quantum Field Theory",
  "authors": [
    "Giovanni Collini"
  ],
  "comment": "This is a preprint (with minor modifications) of my doctoral thesis, which is being submitted to Fakult\\\"at f\\\"ur Physik und Geowissenschaften - Universit\\\"at Leipzig. 169 pages, 3 figures, 2 tables",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (\"phase space\"). His algorithm gives a non-commutative, but associative, product (a so-called \"star-product\") between smooth phase space functions parameterized by Planck's constant $\\hbar$, which is treated as a deformation parameter. In the limit as $\\hbar$ goes to zero, the star product commutator goes to $\\hbar$ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, we develop a generalization of Fedosov's method which applies to the infinite-dimensional symplectic \"manifolds\" that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of this method to more standard perturbative quantization schemes in quantum field theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T15:07:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbative quantum field theory",
      "fedosov quantization",
      "smooth phase space functions",
      "lagrangian field theories",
      "finite-dimensional symplectic manifold"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 169,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309626C",
      "inspire": 1437999
    }
  }
}