A Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills Framework

TL;DR

This paper proposes a unified model of gravity and electroweak interactions using a generalized Yang-Mills framework that includes space-time translational symmetry, resulting in a consistent flat-space theory that aligns with experimental results.

Contribution

It introduces a novel unified model combining gravity and electroweak interactions via a generalized Yang-Mills approach incorporating T(4) symmetry.

Findings

Derivation of wave equations reducing to Hamilton-Jacobi form in geometric optics limit

Introduction of a tensor field ${}{{}{}{}}$ coupling universally to particles

Quantization of the T(4) gravitational gauge field in inertial frames

Abstract

Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators $T_{\mu}(=\p/\p x^{\mu})$ do not have constant matrix representations. By gauging $T(4) \times SU(2) \times U(1)$ in flat space-time, we have a new tensor field $\phi_{\mu\nu}$ which universally couples to all particles and anti-particles with the same constant $g$, which has the dimension of length. In this unified model, the T(4) gauge symmetry dictates that all wave equations of fermions, massive bosons and the photon in flat space-time reduce to a Hamilton-Jacobi equation with the same `effective Riemann metric tensor' in the geometric-optics limit. Consequently, the results are consistent with experiments. We demonstrated that the T(4) gravitational gauge field can be quantized in inertial frames.