{
  "id": "math-ph/0310038",
  "version": "v1",
  "published": "2003-10-20T13:04:08.000Z",
  "updated": "2003-10-20T13:04:08.000Z",
  "title": "Disentangling q-exponentials: A general approach",
  "authors": [
    "C. Quesne"
  ],
  "comment": "LaTeX 2e, 19 pages, no figure",
  "journal": "Int.J.Theor.Phys. 43 (2004) 545-559",
  "doi": "10.1023/B:IJTP.0000028885.42890.f5",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson $q$-exponential of the sum of two non-$q$-commuting operators as an (in general) infinite product of $q$-exponential operators involving repeated $q$-commutators of increasing order, $E_q(A+B) = E_{q^{\\alpha_0}}(A) E_{q^{\\alpha_1}}(B) \\prod_{i=2}^{\\infty} E_{q^{\\alpha_i}}(C_i)$. By systematically transforming the $q$-exponentials into exponentials of series and using the conventional Baker-Campbell-Hausdorff formula, we prove that one can make any choice for the bases $q^{\\alpha_i}$, $i=0$, 1, 2, ..., of the $q$-exponentials in the infinite product. An explicit calculation of the operators $C_i$ in the successive factors, carried out up to sixth order, also shows that the simplest $q$-Zassenhaus formula is obtained for $\\alpha_0 = \\alpha_1 = 1$, $\\alpha_2 = 2$, and $\\alpha_3 = 3$. This confirms and reinforces a result of Sridhar and Jagannathan, based on fourth-order calculations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-20T13:04:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general approach",
      "disentangling q-exponentials",
      "zassenhaus formula",
      "infinite product",
      "conventional baker-campbell-hausdorff formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 631123
    }
  }
}