{
  "id": "1912.12819",
  "version": "v1",
  "published": "2019-12-30T05:33:19.000Z",
  "updated": "2019-12-30T05:33:19.000Z",
  "title": "Deformation quantization and homological reduction of a lattice gauge model",
  "authors": [
    "Markus J. Pflaum",
    "Gerd Rudolph",
    "Matthias Schmidt"
  ],
  "categories": [
    "math-ph",
    "math.DG",
    "math.KT",
    "math.MP",
    "math.SG"
  ],
  "abstract": "For a compact Lie group $G$ we consider a lattice gauge model given by the $G$-Hamiltonian system which consists of the cotangent bundle of a power of $G$ with its canonical symplectic structure and standard moment map. We explicitly construct a Fedosov quantization of the underlying symplectic manifold using the Levi-Civita connection of the Killing metric on $G$. We then explain and refine quantized homological reduction for the construction of a star product on the symplectically reduced space in the singular case. Afterwards we show that for $G = \\operatorname{SU} (2)$ the main hypotheses ensuring the method of quantized homological reduction to be applicable hold in the case of our lattice gauge model. For that case, this implies that the - in general singular - symplectically reduced phase space of the corresponding lattice gauge model carries a star product.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T05:33:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformation quantization",
      "corresponding lattice gauge model carries",
      "star product",
      "quantized homological reduction",
      "standard moment map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}