First followups of April1780 (new LQG) paper A new formulation of LQG was given in the arxiv paper 1004.1780 which is easier for me to remember as 2010 April1780 That was quite possibly the most influential QG paper of the year so since I may want to link to it several times I'll think of it as April1780. We already saw a June paper by Seth Major that is based on this version of LQG and explores a new possibility for testing predictions---another long "lever arm" that magnifies small quantum effects on geometry making them in principle detectable. That is in the phenomenology department so i don't think of it exactly as a followup. Today this came out. It fills in one of the gaps in the April1780 paper: http://arxiv.org/abs/1006.1294 Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory You Ding, Carlo Rovelli 11 pages (Submitted on 7 Jun 2010) "A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case." The boundary geometry is how you get to an analogy with Feynman diagrams and QED. The boundary state is what specifies the "geometry in" and "geometry out" of a quantum geometry dynamics process. And the boundary state of a 4D process is 3D, something that the spin networks of LQG can describe. So the boundary is crucial, it is where a theory like QEG is emerging, where Feynman diagrams are emerging. I mention that to explain why Ding-Rovelli are focusing attention on getting the boundary Hilbert space right.