{
  "id": "2312.06019",
  "version": "v1",
  "published": "2023-12-10T22:21:33.000Z",
  "updated": "2023-12-10T22:21:33.000Z",
  "title": "On the relativistic quantum mechanics of a photon between two electrons in 1+1 dimensions",
  "authors": [
    "Lawrence Frolov",
    "Samuel E. Leigh",
    "A. Shadi Tahvildar-Zadeh"
  ],
  "comment": "25 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two electrons (or alternatively, two positrons). Manifest covariance is achieved using Dirac's formalism of multi-time wave functions, i.e, wave functions $\\Psi(\\textbf{x}_{\\text{ph}},\\textbf{x}_{\\text{e}_1},\\textbf{x}_{\\text{e}_2})$ where $\\textbf{x}_{\\text{ph}},\\textbf{x}_{\\text{e}_1},\\textbf{x}_{\\text{e}_2}$ are generic spacetime events of the photon and two electrons respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifolds $\\{\\textbf{x}_{\\text{ph}}=\\textbf{x}_{\\text{e}_1}\\}$ and $\\{\\textbf{x}_{\\text{ph}}=\\textbf{x}_{\\text{e}_2}\\}$ compatible with conservation of probability current. The corresponding initial-boundary value problem is shown to be well-posed under the additional assumption of anti-symmetry given by the Pauli exclusion principle, and a closed-form solution to the ensuing coupled system of Klein-Gordon and transport equations is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-10T22:21:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q41",
      "81Q05",
      "81V10"
    ],
    "keywords": [
      "relativistic quantum mechanics",
      "wave functions",
      "massive spin one-half dirac particles",
      "lorentz-invariant no-crossing-of-paths boundary condition",
      "identical massive spin one-half dirac"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}