{
  "annotation_id": "73d32f73-b8e2-447d-ad73-d5501e0f0735",
  "date_created": "2026-03-02T18:01:42.652000Z",
  "date_modified": "2026-03-02T18:01:42.652000Z",
  "file_hash": "6d5189c47160fe26a2da9eb6eb95c9d55f9cf3c0168070436604bc25012f9f8c",
  "private": false,
  "record": {
    "abstract": "We provide geometric quantization of the vertical cotangent bundle V^*Q\nequipped with the canonical Poisson structure. This is a momentum phase space\nof non-relativistic mechanics with the configuration bundle Q -\u003e R. The goal is\nthe Schrodinger representation of V^*Q. We show that this quantization is\nequivalent to the fibrewise quantization of symplectic fibres of V^*Q -\u003e R,\nthat makes the quantum algebra of non-relativistic mechanics an instantwise\nalgebra. Quantization of the classical evolution equation defines a connection\non this instantwise algebra, which provides quantum evolution in\nnon-relativistic mechanics as a parallel transport along time.",
    "arxiv_id": "quant-ph/0012036",
    "authors": [
      "G. Giachetta",
      "L. Mangiarotti",
      "G. Sardanashvily"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "title": "Covariant geometric quantization of non-relativistic Hamiltonian   mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0012036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3dee2910-c85c-4d6c-b07b-1e00e425f163",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}