Tetrads in Yang-Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding underlying new geometric local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in 4D Lorentzian spacetimes. In the present paper, a new tetrad is introduced for the Yang-Mills SU(2) × U(1) formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations. New theorems are proved regarding isomorphisms between local internal SU(2) × U(1) groups and local tensor products of spacetime LB1 and LB2 groups of transformations. The new tetrads and the stress-energy tensor allow for introduction of three new local gauge-invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for gauge-invariant diagonalization of the Yang-Mills stress-energy tensor is developed.