{
  "id": "2210.01566",
  "version": "v1",
  "published": "2022-10-04T12:44:22.000Z",
  "updated": "2022-10-04T12:44:22.000Z",
  "title": "Trace class operators and tracial states in p-adic quantum mechanics",
  "authors": [
    "Paolo Aniello",
    "Stefano Mancini",
    "Vincenzo Parisi"
  ],
  "comment": "70 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic numbers, we provide a general definition of a quantum state relying on a general algebraic approach and on a p-adic model of probability theory. As in the standard complex case, a distinguished set of physical states are related to a notion of trace for a certain class of bounded operators and, in fact, we show that one can define a suitable space of trace class operators in the non-Archimedean setting, as well. The analogies, but also the several (highly non-trivial) differences, with respect to the case of standard quantum mechanics in a complex Hilbert space are analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T12:44:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "trace class operators",
      "p-adic quantum mechanics",
      "tracial states",
      "standard quantum mechanics",
      "complex hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 70,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}