fzero said:
LQG proposes to provide a quantum description of gravity. It does not claim to "unify" gravity with the other forces. There have been papers proposing how fermions and the rest of particle physics might be incorporated, but this is not the main goal of the research program. ...
Or a quantum description of geometry-cum-gravity. It's a fair description. The textbooks and review articles by people currently active in the field make this clear. I don't recall anyone saying the main goal was unification.
The other topic of this thread seems to be the Immirzi parameter. Here's a recent paper. E. Livine is one of the longtime leaders in Loop QG--it could be worthwhile taking a look at his reflections on this still somewhat mysterious parameter.
http://arxiv.org/abs/1507.00851
Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
Christoph Charles,
Etera R. Livine
(Submitted on 3 Jul 2015)
8 pages
==sample quote from introduction, pages 1 and 2==
...At a more effective level, it enters the loop quantum gravity dynamics in a non-trivial way and seems to be a crucial parameter in the description of quantum black holes (see the review [6]). It also appears to control the couplings to fermionic field and possible quantum gravity induced CP violation [7–10]. ...
Here, we would like to underline the crucial difference between the role of the Immirzi parameter at the classical level and in the quantum theory. Classically, it appears as a coupling constant in the Holst-Palatini action for the first order formulation of general relativity [3]. In the effective field theory paradigm, one can then investigate its renormalisation flow, together with the Newton’s gravity constant and the cosmological constant, as proposed in [18, 19]. In the full quantum theory,
it appears as a more essential parameter defining directly the fundamental quanta of geometry---scaling the discrete spectra of the area and volume operators---in Planck units. We would like to trace back, in the loop quantization procedure, where the Immirzi parameter acquires this deeper role.
We will use the very simple example of the holonomies of the Ashtekar-Barbero connection on a space-like 3- hyperboloid embedded in flat space-time and look at its dependence on both the hyperboloid curvature and the Immirzi parameter...
...
...
This compactification, which can be understood as the origin of the discrete spectra for areas and volumes, [has the effect] ...that the choice of observables in loop quantum gravity for a fixed Immirzi parameter does not allow to distinguish all points of the classical phase space. In that sense,
the Immirzi parameter quits being a mere coupling constant but appears to play the new effective role of a cut-off, similarly to the energy scale cut-off in usual quantum field theory. This is consistent with the view that it determines the size of discrete quanta of geometry and points towards the perpective that the bare theory would in the “continuum limit” β → 0. Then specific physical situations will require specific values of the Immirzi pa- rameter, which will determine the suitable truncation of the effective corrections to general relativity (resulting from loop quantum gravity) to use in that case. ...
==endquote==
