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Previously, we have developed a general method to construct invariantconserved currents and charges in gravitational theories with Lagrangians thatare invariant under spacetime diffeomorphisms and local Lorentztransformations. This approach is now generalized to the case when the localLorentz group is replaced by an arbitrary local gauge group. The particularexamples include the Maxwell and Yang-Mills fields coupled to gravity withAbelian and non-Abelian local internal symmetries, and the metric-affinegravity in which the local Lorentz spacetime group is extended to the localgeneral linear group.

Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries