Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects
Physics Department, University of Massachusetts Dartmouth, North Dartmouth, 02747-2300, MA, USA
Accepted: 3 February 2011
Published online: 17 March 2011
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.
© Società Italiana di Fisica and Springer, 2011