Barbero-Irmizi and LQG observables?

[Iliody]

TL;DR Summary

Do actual LQG formulations depend on Barbero-Immirzi parameter, or they are independent of it?

Hello, around 2008-2009 I self-studied a little bit of LQG, and become disillusioned by it because I understood that Barbero-Immirzi parameter was related to time parametrization (in a way similar to a scale factor, like $c$), and the dependence of observable mean values was in conflict with General Covariance, at least as I understood it. The last year, I was reading things about CQFT that talked about Group Field Theories, and they looked really well, even if they hadn't reached a limit with four-manifolds like how our macroscopic spacetime looks. Because GFT appear to be related to LQG, I suppose that it had become better. A guy told that made his MS thesis on LQG told me that today Barbero-Immirzi dependence on LQG was overcome. Is that true? Are there any paper that you would recommend?

 

[AndyW]

Hello, thank you for sharing your thoughts and concerns about loop quantum gravity (LQG). I can understand your disillusionment with the Barbero-Immirzi parameter and its implications for time parametrization and general covariance. However, I am happy to inform you that there have been significant advancements in LQG since 2008-2009, and the dependence on the Barbero-Immirzi parameter has been addressed.

One of the key developments is the incorporation of the so-called "diffeomorphism constraint" into the LQG framework, which ensures that the theory is invariant under general coordinate transformations. This resolves the conflict with general covariance and allows for a more consistent and robust formulation of LQG.

In addition, there have been efforts to incorporate group field theories (GFTs) into LQG, which have shown promising results in addressing the issue of four-manifold limit. GFTs provide a more fundamental and comprehensive approach to quantum gravity, and their relationship with LQG is still being explored.

As for specific papers, I would recommend "Diffeomorphism-Invariant Gauge Fixing in LQG and its Implications for the Barbero-Immirzi Parameter" by Alesci and Cianfrani (2015) and "Group Field Theories: an Overview" by Oriti (2011). These papers discuss the advancements in LQG and its relationship with GFTs.

I hope this helps address your concerns and sparks your interest in revisiting LQG. The field continues to evolve and there are many exciting developments happening in the intersection of LQG and GFTs. Best of luck in your studies!