Post-Riemannian Merger of Yang-Mills Interactions with Gravity

Abstract

We show that a post-Riemannian spacetime can accommodate an internal symmetry structure of the Yang-Mills prototype in such a way that the internal symmetry becomes an integral part of the spacetime itself. The construction encrusts the internal degrees of freedom in spacetime in a manner that merges the gauging of these degrees of freedom with the frame geometrical gauges of spacetime. In particular, we prove that the three spacetime structural identities, which now become ``contaminated'' by internal degrees of freedom, remain invariant with respect to internal gauge transformations. In a Weyl Cartan spacetime, the theory regains the original form of Einstein's equations, in which gauge field sources on the r.h.s. determine on the l.h.s the geometry of spacetime and the fields it induces. In the more general case we identify new contributions of weak magnitude in the interaction between the Yang-Mills field and gravity. The merger of spacetime with internal degrees of freedom which we propose here is not constrained by the usual Coleman-Mandula considerations.