{
  "id": "2102.11738",
  "version": "v1",
  "published": "2021-02-23T15:03:33.000Z",
  "updated": "2021-02-23T15:03:33.000Z",
  "title": "Coupled Susy, pseudo-bosons and a deformed $\\mathfrak{su}(1,1)$ Lie algebra",
  "authors": [
    "Fabio Bagarello"
  ],
  "comment": "In press in Journal of Physics A: Mathematical and Theoretical",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In a recent paper a pair of operators $a$ and $b$ satisfying the equations $a^\\dagger a=bb^\\dagger+\\gamma\\1$ and $aa^\\dagger=b^\\dagger b+\\delta\\1$, has been considered, and their nature of ladder operators has been deduced and analysed. Here, motivated by the spreading interest in non self-adjoint operators in Quantum Mechanics, we extend this situation to a set of four operators, $c$, $d$, $r$ and $s$, satisfying $ dc=rs+\\gamma\\1$ and $cd=sr+\\delta\\1$, and we show that they are also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called $\\D$-pseudo bosons. Some examples are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-23T15:03:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebra",
      "coupled susy",
      "pseudo-bosons",
      "ladder operators",
      "non self-adjoint operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}