{
  "id": "quant-ph/0305032",
  "version": "v1",
  "published": "2003-05-06T18:50:24.000Z",
  "updated": "2003-05-06T18:50:24.000Z",
  "title": "Deformed Heisenberg algebra: origin of q-calculus",
  "authors": [
    "P. Narayana Swamy"
  ],
  "comment": "11 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and self-consistent formulation and to show explicitly how the Jackson derivative arises naturally. We utilize a holomorphic representation to arrive at the correct algebra to describe q-deformed bosons. We investigate the algebra of q-fermions and point out how different it is from the theory of q-bosons. We show that the holomorphic representation for q-fermions is indeed feasible in the framework of the theory of generalized fermions. We also examine several different q-algebras in the context of the modified Heisenberg equation of motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-06T18:50:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformed heisenberg algebra",
      "q-calculus",
      "holomorphic representation",
      "q-deformed heisenberg uncertainty relation",
      "intimate connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003quant.ph..5032N"
    }
  }
}