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kodama

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- Thread starter kodama
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In summary, the paper discusses recent developments in canonical gravity that incorporate conformal analysis of gravitational degrees of freedom. This approach has the potential to solve the problem of time in quantum gravity and offers a parameter-free alternative to loop quantum gravity. More recent papers on conformal gravity can be found through a simple Google search or by looking into the LQG topic on this forum.

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kodama

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Physics news on Phys.org

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JorisL

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http://arxiv.org/abs/gr-qc/0512023

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

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kodama

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Conformal gravity is a theory of gravity that attempts to unify general relativity and quantum mechanics by using a conformally invariant action. This means that the theory is invariant under a transformation of the metric that preserves angles but not distances. It is still a developing theory and has not been fully tested or accepted by the scientific community.

Loop quantum gravity is a theory of quantum gravity that attempts to reconcile general relativity and quantum mechanics by quantizing space and time. This theory proposes that space and time are not continuous, but rather made up of tiny, indivisible units called loops. It is still a developing theory and has not been fully tested or accepted by the scientific community.

Conformal gravity and loop quantum gravity differ in their approach to unifying general relativity and quantum mechanics. Conformal gravity uses a conformally invariant action, while loop quantum gravity quantizes space and time. Additionally, conformal gravity is based on classical general relativity, while loop quantum gravity is a purely quantum theory.

Neither conformal gravity nor loop quantum gravity has been widely accepted in the scientific community. Both theories are still developing and have not yet been fully tested or proven. However, some aspects of loop quantum gravity have been incorporated into other theories, such as spin foam models, which have gained more acceptance.

If either conformal gravity or loop quantum gravity is proven to be a valid theory, it could have significant implications for our understanding of the universe. These theories could provide a unified explanation for the behavior of gravity at both the macroscopic and microscopic levels, potentially leading to breakthroughs in fields such as cosmology and quantum mechanics. They could also help to resolve long-standing problems in physics, such as the singularity at the center of black holes.

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