Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects

TL;DR

This paper develops a Yang-Mills gravity theory in flat space-time that produces an effective curved space-time for classical objects in the geometric-optics limit, aligning with general relativity predictions.

Contribution

It introduces a consistent Yang-Mills gravity framework with a derived effective metric tensor that explains classical motion and photon behavior in a flat space-time setting.

Findings

Emergence of an effective Riemannian metric in the geometric-optics limit.

Feynman rules for graviton-fermion interactions including gauge parameters.

Demonstration of classical equations of motion as wave equation limits.

Abstract

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.