{
  "annotation_id": "2d8c6052-6ac5-422d-abe4-ef53a76b3063",
  "date_created": "2026-03-02T18:01:52.365000Z",
  "date_modified": "2026-03-02T18:01:52.365000Z",
  "file_hash": "0bc6f654bf8ce58899c390abe6ed7ec26d60a40583a3be3e7c93d2b1a0ea6b3f",
  "private": false,
  "record": {
    "abstract": "We show that the requirement of manifest coordinate invariance of\nperturbatively defined quantum-mechanical path integrals in curved space leads\nto an extension of the theory of distributions by specifying unique rules for\nintegrating products of distributions. The rules are derived using equations of\nmotion and partial integration, while keeping track of certain minimal features\nstemming from the unique definition of all singular integrals in 1 - epsilon\ndimensions. Our rules guarantee complete agreement with much more cumbersome\ncalculations in 1- epsilon dimensions where the limit epsilon --\u003e 0 is taken at\nthe end. In contrast to our previous papers where we solved the same problem\nfor an infinite time interval or zero temperature, we consider here the more\ninvolved case of finite-time (or non-zero temperature) amplitudes.",
    "arxiv_id": "quant-ph/0208067",
    "authors": [
      "H. Kleinert",
      "A. Chervyakov"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1142/S0217751X02006146",
    "journal_ref": "Int.J.Mod.Phys.A17:2019,2002",
    "title": "Integrals over Products of Distributions from Manifest Coordinate   Invariance of Perturbation Expansions of Path Integrals in Curved Space",
    "url": "https://arxiv.org/abs/quant-ph/0208067"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4203fd36-7abe-4f7e-8b67-f1d8c37895ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}