{
  "id": "2301.05467",
  "version": "v1",
  "published": "2023-01-13T10:40:27.000Z",
  "updated": "2023-01-13T10:40:27.000Z",
  "title": "Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion",
  "authors": [
    "Folkert Kuipers"
  ],
  "comment": "59+50 pages",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "gr-qc",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-13T10:40:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motion",
      "stochastic mechanics",
      "unification",
      "non-relativistic quantum mechanics",
      "consistent path integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}