{
  "id": "2409.10495",
  "version": "v1",
  "published": "2024-09-16T17:27:50.000Z",
  "updated": "2024-09-16T17:27:50.000Z",
  "title": "On the thermodynamic limit of interacting fermions in the continuum",
  "authors": [
    "Oliver Siebert"
  ],
  "comment": "20 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "We study the dynamics of non-relativistic fermions in $\\mathbb R^d$ interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we identify an extension of the CAR algebra where the dynamics acts as a group of *-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we identify a suitable dense subalgebra where the time evolution is also strongly continuous. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-16T17:27:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermodynamic limit",
      "interacting fermions",
      "construct kms states",
      "dynamics acts",
      "non-relativistic fermions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}