Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity

TL;DR

This work presents an independent derivation of the EPR spinfoam model by treating the simplicity constraints as second-class and enforcing them weakly via coherent intertwiners, thereby avoiding the over-constrained boundary space of Barrett-Crane. It introduces an enlarged Hilbert space of symmetric intertwiners where the constraints hold in expectation, and constructs coherent simple intertwiners whose tetrahedral states reproduce the EPR intertwiners with a Spin(4) averaging. The resulting 4-simplex amplitudes align with the EPR proposal, expressed in a coherent-spin-basis rather than the traditional 15j basis, and clarifies a sign ambiguity corresponding to two classical sectors. The analysis sets the stage for asymptotic studies and graviton propagator checks to confirm the correct gravitational degrees of freedom and semiclassical limit.

Abstract

We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier in [arXiv:0705.0674], we show that the EPR model realizes a consistent imposition of the simplicity constraints implementing general relativity from a topological BF theory.