{
  "annotation_id": "801ac649-e31d-4788-953e-5bbab3f3dd48",
  "date_created": "2026-03-02T18:01:14.818000Z",
  "date_modified": "2026-03-02T18:01:14.818000Z",
  "file_hash": "8e7ea111dbb2f186456de4b48e250214b5db4452e1e29762873c14f5a5c572f9",
  "private": false,
  "record": {
    "abstract": "Multipole expansions depend on the coordinate system, so that coefficients of\nmultipole moments can be set equal to zero by an appropriate choice of\ncoordinates. Therefore, it is meaningless to say that a physical system has a\nnonvanishing quadrupole moment, say, without specifying which coordinate system\nis used. (Except if this moment is the lowest non-vanishing one.) This result\nis demonstrated for the case of two equal like electric charges. Specifically,\nan adapted coordinate system in which the potential is given by a monopole term\nonly is explicitly found, the coefficients of all higher multipoles vanish\nidentically. It is suggested that this result can be generalized to other\npotential problems, by making equal coordinate surfaces coincide with the\npotential problem\u0027s equipotential surfaces.",
    "arxiv_id": "physics/0701021",
    "authors": [
      "Lior M. Burko"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1088/0143-0807/28/3/021",
    "journal_ref": "European Journal of Physics 28 (2007) 593-602",
    "title": "Multipole structure and coordinate systems",
    "url": "https://arxiv.org/abs/physics/0701021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f87ac7c8-f8b8-47c1-99f4-4276df4dbd65",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}