{
  "id": "2303.00156",
  "version": "v2",
  "published": "2023-03-01T01:04:54.000Z",
  "updated": "2023-06-22T01:04:12.000Z",
  "title": "An unitary representation of inhomogeneous ${\\rm SL}(2,\\mathbb{C})$ using surfaces in $\\mathbb{R}^4$",
  "authors": [
    "Adrian P. C. Lim"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We will construct a separable Hilbert space for which the inhomogeneous ${\\rm SL}(2,\\mathbb{C})$ acts on it unitarily. Each vector in this Hilbert space is described by a (rectangular) surface in $\\mathbb{R}^4$, for which a vector field is defined on it. The inner product on this Hilbert space is defined via a surface integral, which is associated with the area of the surface.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-06-22T01:04:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E43"
    ],
    "keywords": [
      "unitary representation",
      "inhomogeneous",
      "surface integral",
      "inner product",
      "vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}