{
  "id": "2307.03282",
  "version": "v1",
  "published": "2023-07-06T20:35:59.000Z",
  "updated": "2023-07-06T20:35:59.000Z",
  "title": "Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics and Schrödinger equations",
  "authors": [
    "Nicoló Drago",
    "Sonia Mazzucchi",
    "Valter Moretti"
  ],
  "comment": "50 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral, and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schr\\\"odinger equation, where the Laplace-Beltrami operator coincides with the second order Casimir operator of the group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-06T20:35:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact lie groups",
      "bi-invariant riemannian metrics",
      "feynman path integral",
      "schrödinger equations",
      "second order casimir operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}