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

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.PACS 11.15.-q, Gauge field theory, 04.20.Cv -Fundamental problem.

The S-matrix and graviton self-energy in quantum Yang-Mills gravity

“…[9] Similar mechanism of cancellation occurs in any theory with gauge symmetry or distorted gauge symmetry, and in Yang-Mills gravity. [11,12,13] We follow Faddeev and Popov's approach to discuss how to fix a gauge for all times with the help of path integrals and derived the effective Lagrangian for quantum Yang-Mills gravity. [10,11] From the action (1) with the Lagrangian (2) and the gauge-fixing terms (3), we derived the Yang-Mills field equation…”

“…The matrix U in (13) can be obtained by expressing the Lagrangian for the Feynman-DeWitt-Mandelstam (FDM) ghost fields V µ and V ν in the following form,…”

“…Thus, the rules for Feynman diagrams in quantum Yang-Mills gravity can be derived from the total Lagrangian (22). [13] 4 Unitarity of the S-matrix and FDM ghost particles…”

“…The generating functional for connected Green's functions in gauge invariant gravity can be defined after the gauge condition is specified. [13] Similarly, in Yang-Mills gravity the generating functional for connected Green's functions (or the vacuum-to-vacuum amplitude) (19) can be written as [12] W…”

“…Its amplitude, denoted by S µναβ 1 (p), can be calculated by using the Feynman rules with ξ = 2 in the gauge-fixing Lagrangian (3), for simplicity. [13] The process (30) leads to the following amplitude for the graviton selfenergy,…”