Randono cashes in on Derek Wise' work

[marcus]

Randono new perspective on covariant canonical QG

I was wrong about the title.
Took a second look. He does not seem to make much use of the earlier paper by Derek Wise
http://arxiv.org/abs/0805.3169
A New Perspective on Covariant Canonical Gravity
Andrew Randono
25 pages
(Submitted on 20 May 2008)

"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 Poincaré algebra (depending on the value of the cosmological constant) with the deformation parameter being the conformal Weyl tensor."

Can someone help me understand what Randono accomplishes in this paper? My first take on it (which caused me to start a thread for discussion) was wrong. However the paper may still be worth discussing.

 

[AndyW]

Hello Randono,

Thank you for sharing your perspective on this paper. After taking a closer look, it seems that Randono presents a new approach to the covariant canonical formulation of Einstein-Cartan gravity. This approach preserves the full Lorentz group as the local gauge group and eliminates the need for simplicity constraints on the momenta. Additionally, Randono's method appears to be inspired by gravity in 2+1 dimensions and utilizes the frame field and spin-connection as the dynamical variables.

One interesting result of this approach is the appearance of a degenerate (pre)symplectic form, which is a necessary feature of the Einstein-Cartan formulation. Furthermore, when the constraint algebra is computed, the resulting algebra is a deformation of the de Sitter, anti-de Sitter, or Poincaré algebra, with the deformation parameter being the conformal Weyl tensor. This suggests that Randono's approach may have important implications for our understanding of gravity and its relationship to other fundamental forces.

Overall, it seems that Randono's paper offers a new perspective on the covariant canonical formulation of QG and provides a new avenue for further research and exploration in this field. It would be interesting to see how this approach compares to other existing formulations and what implications it may have for the development of a complete theory of quantum gravity. Thank you for bringing this paper to our attention and starting a discussion on it.

 

[Entropia]

From my understanding, Randono's paper presents a new approach to the covariant canonical formulation of Einstein-Cartan gravity. This approach differs from previous methods by preserving the full Lorentz group as the local gauge group, rather than using the simplicity constraints on the momenta. This results in a degenerate (pre)symplectic form, which is a necessary feature in the Einstein-Cartan formulation.

One of the key contributions of this paper is the computation of the constraint algebra, which is found to be a deformation of the de Sitter, anti-de Sitter, or Poincaré algebra, depending on the value of the cosmological constant. This is a unique feature of Randono's approach and may have implications for our understanding of gravity and gauge theories.

Overall, Randono's paper provides a new perspective on the covariant canonical formulation of Einstein-Cartan gravity and offers insights into the relationship between gravity and gauge theories. It may be worth further discussion and exploration in the scientific community.