{
  "id": "2008.11496",
  "version": "v1",
  "published": "2020-08-26T11:23:08.000Z",
  "updated": "2020-08-26T11:23:08.000Z",
  "title": "Bargmann-Fock sheaves on Kähler manifolds",
  "authors": [
    "Kwokwai Chan",
    "Naichung Conan Leung",
    "Qin Li"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.DG",
    "hep-th",
    "math.CV",
    "math.QA"
  ],
  "abstract": "Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product $\\star$ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf of Bargmann-Fock modules over the Weyl bundle of a K\\\"ahler manifold $X$ equipped with a compatible Fedosov abelian connection, and show that the sheaf of flat sections forms a module sheaf over the sheaf of deformation quantization algebras defined $(C^\\infty_X[[\\hbar]], \\star)$. This sheaf can be viewed as the $\\hbar$-expansion of $L^{\\otimes k}$ as $k \\to \\infty$, where $L$ is a prequantum line bundle on $X$ and $\\hbar = 1/k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-26T11:23:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler manifolds",
      "bargmann-fock sheaves",
      "weyl bundle",
      "deformation quantization algebras",
      "flat sections forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}