Conservation laws and integrability conditions for gravitational and Yang-Mills field equations (Q1081866)

We show that expressed in the appropriate principal bundles, the gravitational and Yang-Mills fields equations are equivalent to integrability conditions and that the latter can also be interpreted, using local sections, as conservation equations of the local pseudo- densities of energy-momentum and Yang-Mills charge respectively. These densities can be related using a Kaluza-Klein unification.