{
  "id": "2204.04854",
  "version": "v1",
  "published": "2022-04-11T03:45:32.000Z",
  "updated": "2022-04-11T03:45:32.000Z",
  "title": "A Uniqueness Result for the Calderon Problem for $U(N)$-connections coupled to spinors",
  "authors": [
    "Carlos Valero"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor series of the metric and connection at the boundary. We go on to show that if two real-analytic connections couple to a spinor via the Yang--Mills--Dirac equations with appropriate boundary conditions, and have equal Dirichlet-to-Neumann maps, then the two connections are locally gauge equivalent. In the abelian case, the connections are globally gauge equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-11T03:45:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calderon problem",
      "uniqueness result",
      "appropriate boundary conditions",
      "equal dirichlet-to-neumann maps",
      "real-analytic connections couple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}