{
  "id": "math-ph/0106008",
  "version": "v3",
  "published": "2001-06-12T06:12:51.000Z",
  "updated": "2001-11-02T09:35:08.000Z",
  "title": "Complex Structures in Electrodynamics",
  "authors": [
    "Stoil Donev"
  ],
  "comment": "Latex2e, 19 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure $\\mathcal{I}$ participates implicitly in the equations and its presence is responsible for the so called duality invariance. We give a new form of the equations showing explicitly the participation of $\\mathcal{I}$. In the 4-dimensional formulation the complex structure is extracted directly from the equations, it appears as a linear map $\\Phi$ in the space of 2-forms on $\\mathbb{R}^4$. It is shown also that $\\Phi$ may appear through the equivariance properties of the new formulation of the theory. Further we show how this complex structure $\\Phi$ combines with the Poincare isomorphism $\\mathfrak{P}$ between the 2-forms and 2-tensors to generate all well known and used in the theory (pseudo)metric constructions on $\\mathbb{R}^4$, and to define the conformal symmetry properties. The equations of Extended Electrodynamics (EED) do not also need these pseudometrics as beforehand necessary structures. A new formulation of the EED equations in terms of a generalized Lie derivative is given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-11-02T09:35:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "78A02",
      "78A25",
      "78A97"
    ],
    "keywords": [
      "complex structure",
      "formulation",
      "conformal symmetry properties",
      "standard form",
      "maxwell equations"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1224856,
      "adsabs": "2001math.ph...6008D"
    }
  }
}