{
  "id": "1110.6607",
  "version": "v1",
  "published": "2011-10-30T13:12:25.000Z",
  "updated": "2011-10-30T13:12:25.000Z",
  "title": "Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics",
  "authors": [
    "Alexander Wilce"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations between, probabilistic models. The key tool is the Koecher-Vinberg Theorem, which identifies formally real Jordan algebras with finite-dimensional order-unit spaces having homogeneous, self-dual cones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-30T13:12:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jordan structure",
      "quantum mechanics",
      "identifies formally real jordan algebras",
      "self-duality",
      "finite-dimensional quantum theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6607W"
    }
  }
}