{
  "annotation_id": "392d8e8f-29ee-4175-a0ed-a020b33989b5",
  "date_created": "2026-03-02T18:00:01.592000Z",
  "date_modified": "2026-03-02T18:00:01.592000Z",
  "file_hash": "4382e328b31a2f3a85a56a9a1dee7bc51a1532c2bef623bbeb1a94bf1cf043b4",
  "private": false,
  "record": {
    "abstract": "Generalised Dyson boson-fermion mappings are considered. These are techniques\nused in the analysis of the quantum many-body problem, and are instances of\nso-called boson expansion methods. A generalised Dyson boson-fermion mapping is\na one-to-one linear but non-unitary operator that can be applied to vectors\nrepresenting the states of a many-fermion system. A vector representing a\nfermion system maps onto a vector that represents a state of a many-body system\nthat contains both bosons and fermions. The motivation for doing such a mapping\nis the hope that it will reveal some property of the system that simplifies its\nanalysis and that was hidden in the original form. The aims of this text are to\nreview the theory of generalized Dyson boson-fermion mappings and to find a\nuseful application for a generalized Dyson boson-fermion mapping, by\nconsidering a non-trivial model, namely the Richardson model for\nsuperconductivity. It is the first time that a boson expansion technique is\nimplemented for a system where the roles of both collective and non-collective\nfermion pairs are important. The Dyson mapping uncovers non-trivial properties\nof the system that aid the construction of time-independent as well as\ntime-dependent perturbation expansions. The time-independent expansions agree\nwith results that other authors have obtained through methods other than boson\nexpansions. The time-dependent expansions might in future prove useful in\nunderstanding aspects of the dynamics of ultra-cold fermi gases, when\ntime-dependent magnetic fields are used to vary the atom-atom interaction\nstrenght.",
    "arxiv_id": "nucl-th/0411059",
    "authors": [
      "I. Snyman"
    ],
    "categories": [
      "nucl-th",
      "cond-mat.supr-con"
    ],
    "title": "Analysis and Applications of the Generalised Dyson Mapping",
    "url": "https://arxiv.org/abs/nucl-th/0411059"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5f6717f6-5c23-4d3e-bf7f-77f03d7147b9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}