Andrew Randono 2008 Class. Quantum Grav. 25 235017 doi:10.1088/0264-9381/25/23/235017
Andrew Randono
Show affiliationsWe 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 Poincaré algebra (depending on the value of the cosmological constant) with the deformation parameter being the conformal Weyl tensor.
04.20.Fy Canonical formalism, Lagrangians, and variational principles
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
83C45 Quantization of the gravitational field
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
Issue 23 (7 December 2008)
Received 18 July 2008, in final form 30 September 2008
Published 17 November 2008
Andrew Randono 2008 Class. Quantum Grav. 25 235017
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