General relativity and the U(1) gauge group

Abstract

We show that gravity together with curved spacetime can emerge, at the microscopic scale, from a U(1) gauge field. The gauge boson that carries gravity, of elementary particles, is proved to be a spin one massless and electrically neutral vector particle dubbed the "gamma boson" referring to the Dirac matrices, gamma_mu, which are promoted to be the quantum field for gravity at the scale of elementary particles. Instead, the graviton appears merely as a tensor bound state of two gamma bosons in the same spin eigenstate, by referring to the relation g_mu nu = 1/2 (gamma_mu gamma_nu + gamma_nu gamma_mu) and the metric ds^2 = g_mu nu dx^mu dx^nu = (gamma_alpha dx^alpha)^2. Consequently, like the electroweak theory and quantum chromodynamics, gravity may be formalized as a Yang-Mills theory. As a consequence, there is no need of the Higgs field or any symmetry breaking mechanism to generate the mass of fundamental particles. We show that one can get rid of the Yukawa couplings in favor of the covariant derivative. Finally, a set of partial differential equations that is equivalent to Einstein equations is established for the gamma boson. Static spherical symmetric external solutions leading to the Schwarzschild metric are found by solving the latter neglecting the mass density of the gravitational field itself. Taking into account the latter involves a departure from the Schwarzschild solution that may be tested by laboratory experiments or astrophysical observations.