{
  "id": "1808.01978",
  "version": "v1",
  "published": "2018-08-06T16:13:58.000Z",
  "updated": "2018-08-06T16:13:58.000Z",
  "title": "Gauge theory of Gravity based on the correspondence between the $1^{st}$ and the $2^{nd}$ order formalisms",
  "authors": [
    "David Benisty",
    "Eduardo I. Guendelman"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "A covariant canonical gauge theory of gravity free from torsion is studied. Using a metric conjugate momentum and a connection conjugate momentum, which takes the form of the Riemann tensor, a gauge theory of gravity is formulated, with form-invariant Hamiltonian. Through the introduction of the metric conjugate momenta, a correspondence between the Affine-Palatini formalism and the metric formalism is established, since when the dynamical gravitational Hamiltonian $\\tilde{H}_{Dyn}$ does not depend on the metric conjugate momenta, a metric compatibility is obtained from the equation of motions and the energy momentum is covariant conserved. When the gravitational Hamiltonian $\\tilde{H}_{Dyn}$ is depend on the metric conjugate momentum, an extension to the metric compatibility comes from the equation of motions and the energy momentum covariant conservation violates. For a sample of the $\\tilde{H}_{Dyn}$ which consists a quadratic term of the connection conjugate momentum, the effective Lagrangian has the Einstein Hilbert term with a quadratic Riemann term in the second order formalism. A bouncing inflation, in the context of cosmological solutions of this action is briefly discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-06T16:13:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauge theory",
      "metric conjugate momentum",
      "order formalism",
      "connection conjugate momentum",
      "correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}