Exact Space-Time Gauge Symmetry of Gravity, Its Couplings and Approximate Internal Symmetries in a Total-Unified Model

Abstract

The gravitational field is the manifestation of space-time translational (T_4) gauge symmetry, which enables the gravitational interaction to be unified with the strong and the electroweak interactions. Such a total-unified model is based on a generalized Yang-Mills framework in flat space-time. Following the idea of Glashow-Salam-Ward-Weinberg, we gauge the groups T_4 × (SU_3)_(color) × SU_2 × U_1 × U_(1b) on equal-footing, so that we have the total-unified gauge covariant derivative δ_μ = ∂μ - igϕ _μ^νpv + ig_sG _μ^a (λ^a/2) + ifW_μ^kt^k + if'U_μt_o + ig_bB_μ. The generators of the external T_4 group have the representation p_μ = i∂_μ, which differs from the other generators of all the other internal groups, which have constant matrix representations. Consequently, the total-unified model leads to the following new results: (a) All internal (SU_3)_(color), SU_2, U_1, and baryonic U_(1b) gauge symmetries have extremely small violations due to the gravitational interaction. (b) The T_4 gauge symmetry remains exact and dictates the universal coupling of gravitons. (c) Such a gravitational violation of internal gauge symmetries leads to modified eikonal and Hamilton-Jacobi type equations, which are obtained in the geometric-optics limit and involve effective Riemann metric tensors. (d) The rules for Feynman diagrams involving new couplings of the photon-graviton, gluon-graviton, and quark-graviton are obtained.