Quantum Yang-Mills gravity in flat space-time and effective curved   space-time for motions of classical objects
  Yang-Mills gravity with translational gauge group T(4) in flat space-time implies a simple self-coupling of gravitons and a truly conserved energy-momentum tensor. Its consistency with experiments crucially depends on an interesting property that an `effective Riemannian metric tensor' emerges in and only in the geometric-optics limit of the photon and particle wave equations. We obtain Feynman rules for a coupled graviton-fermion system, including a general graviton propagator with two gauge parameters and the interaction of ghost particles. The equation of motion of macroscopic objects, as an N-body system, is demonstrated as the geometric-optics limit of the fermion wave equation. We discuss a relativistic Hamilton-Jacobi equation with an `effective Riemann metric tensor' for the classical particles. 
Jong-Ping Hsu
gr-qc hep-th