Wang: Towards Conformal Loop Quantum Gravity

[marcus]

https://www.physicsforums.com/showpost.php?p=847769&postcount=426

http://arxiv.org/abs/gr-qc/0512023
Towards conformal loop quantum gravity
Charles H.-T. Wang
6 pages, 1 figure, Talk given at Constrained Dynamics and Quantum Gravity 05, Cala Gonone, Sardinia, Italy, 12-16 September 2005
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric and the triad levels. At the metric level, it is shown that by extending the Arnowitt-Deser-Misner (ADM) phase space of general relativity (GR), a conformal form of geometrodynamics can be constructed. In addition to the Hamiltonian and diffeomorphism constraints, an extra first class constraint is introduced to generate conformal transformations. This phase space consists of York's mean extrinsic curvature time, conformal three-metric and their momenta. At the triad level, the phase space of GR is further enlarged by incorporating spin-gauge as well as conformal symmetries. This leads to a canonical formulation of GR using a new set of real spin connection variables. The resulting gravitational constraints are first class, consisting of the Hamiltonian constraint and the canonical generators for spin-gauge and conformorphism transformations. The formulation has a remarkable feature of being parameter-free. Indeed, it is shown that a conformal parameter of the Barbero-Immirzi type can be absorbed by the conformal symmetry of the extended phase space. This gives rise to an alternative approach to loop quantum gravity that addresses both the conceptual problem of time and the technical problem of functional calculus in quantum gravity."

this guy is a dark horse. I would appreciate help evaluating this work if anyone has any ideas.

what is wrong with Wang's approach?
or even simpler, what IS Wang's approach, what is the essential, what makes it different?

how can one even consider using conformal diffeomorphisms instead of ordinary? Is this what he is doing?

He delivered this paper at the September Quantum Gravity conference but he is not really one of the regulars---not a gravitist. he works on all kinds of other physics as well. He is at a good place in the UK though. Perspective on this? Comments?

 

[marcus]

also maybe look at Wang's track record in publishing papers on his conformal QG
he has already TWO about this IN PHYSICAL REVIEW D
and he has a third one that was accepted for publication in "Classical and Quantum Gravity" 2005
http://arxiv.org/abs/gr-qc/0406079
Nonlinear quantum gravity on the constant mean curvature foliation
Charles H-T Wang
14 pages. Classical and Quantum Gravity (To appear)
Class.Quant.Grav. 22 (2005) 33-45
"A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory."
unless one of us can come up with a reason not to consider the Wang QG approach we should probably get it on the radar and understand it a little.