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Summary:
Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms lying in the kernel of generalized Jacobi morphisms satisfy Bergmann-Bianchi identities and thus are generators of canonical covariant currents and superpotentials. As a consequence of the second Noether theorem, we further show that there exists a covariantly conserved current associated with the Lagrangian obtained by contracting the Euler-Lagrange morphism with a gauge-natural Jacobi vector field. We use as fundamental tools an invariant decomposition formul!
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