A New Perspective on Covariant Canonical Gravity

TL;DR

This paper introduces a covariant canonical formulation of Einstein-Cartan gravity that maintains the full Lorentz symmetry, utilizing gauge theory insights and revealing a deformed constraint algebra influenced by the Weyl tensor.

Contribution

It presents a novel covariant canonical approach that avoids simplicity constraints and uncovers a deformation of the gauge algebra linked to the Weyl tensor.

Findings

The formulation preserves full Lorentz invariance.

The constraint algebra is a deformation of standard gauge algebras.

The approach simplifies the dynamical variables to frame field and spin-connection.

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.