Loop-quantum-gravity vertex amplitude

Phys Rev Lett. 2007 Oct 19;99(16):161301. doi: 10.1103/PhysRevLett.99.161301. Epub 2007 Oct 16.

Abstract

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.