{
  "id": "2208.03487",
  "version": "v1",
  "published": "2022-08-06T10:09:24.000Z",
  "updated": "2022-08-06T10:09:24.000Z",
  "title": "Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons",
  "authors": [
    "Sascha Lill"
  ],
  "comment": "20 pages, 2 figures, contribution to the Proceedings of the Intensive Period \"INdAM Quantum Meetings (IQM22)\" at Politecnico di Milano, March - May 2022",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct an extension of Fock space and prove that it allows for implementing bosonic Bogoliubov transformations in a certain extended sense. While an implementation in the regular sense on Fock space is only possible if a certain operator $ v^* v $ is trace class (this is the well-known Shale-Stinespring condition), the extended implementation works without any restrictions on this operator. This generalizes a recent result of extended implementability, which required $ v^* v $ to have discrete spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-06T10:09:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fock space",
      "implementing bosonic bogoliubov transformations",
      "regular sense",
      "extended implementation works",
      "discrete spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}