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 spacetime translational group T(4), whose generators Tμ ( = ∂/∂xμ) do not have constant matrix representations. By gauging T(4) × SU(2) × U(1) in flat spacetime, we have a new tensor field ϕμν 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 spacetime 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.