{
  "annotation_id": "435f935a-052f-4d5e-9801-bf651ac3d810",
  "date_created": "2026-03-02T18:00:43.258000Z",
  "date_modified": "2026-03-02T18:00:43.258000Z",
  "file_hash": "ec17901663bf7cef2757418739eb19f1a10c52aa085359b921bad2a8babeae48",
  "private": false,
  "record": {
    "abstract": "One set of the Ziolkowski family of exact solutions of the wave equation are\nshown to represent pulses propagating with momentum smaller than energy/c. This\nis explicitly demonstrated for special cases by calculating the total\nelectromagnetic momentum and energy. Since the ratio of momentum to energy is a\nconstant smaller than 1/c, there exists a Lorentz transformation to a frame in\nwhich the total momentum is zero. In the zero-momentum frame the fields are\nthose of an annular pulse converging onto or diverging from a focal region.",
    "arxiv_id": "physics/0304022",
    "authors": [
      "John Lekner"
    ],
    "categories": [
      "physics.optics",
      "physics.gen-ph"
    ],
    "doi": "10.1088/1464-4258/5/4/101",
    "title": "Electromagnetic pulses which have a zero momentum frame",
    "url": "https://arxiv.org/abs/physics/0304022"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6eb44943-103b-4273-9871-52758d5d6d6f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}