I have finished a quick first reading of the rovelli at all paper ingraviton propagator http://arxiv.org/gr-qc/0604044 I couldn´t dive too much into the details because spin foams was a prerequisite and i only could do an equally fast reading of the alejandro perez review of the subjecto (i am tourning into the math exams now and i have less time for LQG). But still with these porr knowledge i guess an aspecto is not trated as deep as it deserves in these articles. I men,they get second order in a [tex]\lamdba[\tex] constant wich appears in the Barret-Crane model, that is, it multiplies te "interaction" term. I didn´t see it firmly stablished but i guess that is somewhat equivalent to a second order in a series in the usual gravity G constant.That is, second order of perturbation theory in linear perturbative quantum gravity. If these is true these would mean that they second order graviton propagator would correspond to the renormalized (loosely speaking) second order graviton propagator of the "naive" linear quantum gravity, isn´t it? That would be a mayor succes because, as it is well known, linear quantum gravity isn´t renormalizable. So LQG would be, among other things, a way of ding renormalization in linear quantum gravity (i can´t brief it because it also would be LQG :uhh:). Of course one of the mayor claims of loop QG is that you don´t need renormalization because it provides a natural cut´.off and et, etc. As i said these doubt come from an inadequate fast rading. Hope not too disturb people if i made a too stupid question.