Conformal gravity vs loop quantum gravity

[kodama]

if conformal gravity is a successful research program, what would its implications be for loop quantum gravity? can conformal gravity be loop quantized? can loop quantum gravity be made to respect conformal invariance? or are the two mutually exclusive?

 

[JorisL]

Let me start with googling for you (click the link you might learn a thing) http://lmgtfy.com/?q=Conformal+Loop+quantum+gravity

http://arxiv.org/abs/gr-qc/0512023
Towards conformal loop quantum gravity
Charles H.-T. Wang
(Submitted on 5 Dec 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.

I haven't looked into this but as you see this is a fairly recent development. Given that it's also the first hit on google (second being the same paper on the iopscience website) I would say this is a good starting point.
Next you can look into the LQG topic in this subforum as well as the MIP polls marcus composes each quarter.

Joris

 

[kodama]

that paper was written in 2005 and obviously many recent papers on conformal gravity were written after 2012