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We calculate the most divergent contribution to the nondegenerate sector of the self-energy (or ``melonic'') graph in the context of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov spin foam model of quantum gravity. We find that such a contribution is logarithmically divergent in the cutoff over the SU (2) representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the noncommutativity of the Engle-Pereira-Rovelli-Livine and Freidel-Krasnov Y_ map with the projector onto SL (2, C) -invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, their geometrical interpretation, and the physical consequences of our result.
Aldo Riello (Mon,) studied this question.