A New Perspective on Covariant Canonical Gravity

Abstract

We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the relation between gravity and a general gauge theory. The dynamical variables are simply the frame field and the spin-connection pulled-back to the hypersurface, thereby eliminating the need for simplicity constraints on the momenta. A consequence of this is a degenerate (pre)symplectic form, which appears to be a necessary feature of the Einstein-Cartan formulation. A new feature unique to this approach arises when the constraint algebra is computed: the algebra is a deformation of the de Sitter, anti-de Sitter, or Poincar\'{e} algebra (depending on the value of the cosmological constant) with the deformation parameter being the conformal Weyl tensor.