{
  "id": "0802.4235",
  "version": "v1",
  "published": "2008-02-28T16:46:31.000Z",
  "updated": "2008-02-28T16:46:31.000Z",
  "title": "Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry",
  "authors": [
    "P. Kocabova",
    "P. Stovicek"
  ],
  "doi": "10.1063/1.2898484",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider an invariant quantum Hamiltonian $H=-\\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\\tilde{M}$ with a countable discrete symmetry group $\\Gamma$. Typically, $\\tilde{M}$ is the universal covering space of a multiply connected Riemannian manifold $M$ and $\\Gamma$ is the fundamental group of $M$. On the one hand, following the basic step of the Bloch analysis, one decomposes the $L^{2}$ space over $\\tilde{M}$ into a direct integral of Hilbert spaces formed by equivariant functions on $\\tilde{M}$. The Hamiltonian $H$ decomposes correspondingly, with each component $H_{\\Lambda}$ being defined by a quasi-periodic boundary condition. The quasi-periodic boundary conditions are in turn determined by irreducible unitary representations $\\Lambda$ of $\\Gamma$. On the other hand, fixing a quasi-periodic boundary condition (i.e., a unitary representation $\\Lambda$ of $\\Gamma$) one can express the corresponding propagator in terms of the propagator associated to the Hamiltonian $H$. We discuss these procedures in detail and show that in a sense they are mutually inverse.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-28T16:46:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifold",
      "generalized bloch analysis",
      "quasi-periodic boundary condition",
      "propagator",
      "unitary representation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Physics",
      "year": 2008,
      "month": "Mar",
      "volume": 49,
      "number": 3,
      "pages": "033518"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 791096,
      "adsabs": "2008JMP....49c3518K"
    }
  }
}