{
  "annotation_id": "b167ad95-3a44-4231-b53a-ddeaa9d3e961",
  "date_created": "2026-03-02T18:00:43.474000Z",
  "date_modified": "2026-03-02T18:00:43.474000Z",
  "file_hash": "7185d72aa495ff4567918237a2bd84430eb1cf16bd7d371e136cd6951878582d",
  "private": false,
  "record": {
    "abstract": "The definition and properties of the Euler-Lagrange cohomology groups\n$H^{2k-1}$, $1 \\leqslant k \\leqslant n$, on a symplectic manifold $({\\cal\nM}^{2n},\\omega)$ are given and studied. For $k = 1$ and $k = n$, they are\nisomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\\cal\nM}^{2n})$ and $H_{dR}^{2n-1}({\\cal M}^{2n})$, respectively. The other\nEuler-Lagrange cohomology groups are different from either the de Rham\ncohomology groups or the harmonic cohomology groups on $({\\cal\nM}^{2n},\\omega)$, in general. The general volume-preserving equations on\n$({\\cal M}^{2n},\\omega)$ are also presented from cohomological point of view.\nIn the special cases, these equations become the ordinary canonical equations\nin the Hamilton mechanics. Therefore, the Hamilton mechanics has been\ngeneralized via the cohomology.",
    "arxiv_id": "physics/0304074",
    "authors": [
      "Han-Ying Guo",
      "Jianzhong Pan",
      "Ke Wu",
      "Bin Zhou"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "title": "The Euler-Lagrange Cohomology Groups on Symplectic Manifolds",
    "url": "https://arxiv.org/abs/physics/0304074"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "efe6d537-100d-4036-ae36-767d0aed729f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}