Abstract
Given a principal bundle P→ M we classify all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms. These are shown to be variationally trivial and to give constant actions that equal the characteristic numbers of P if dim M is even and zero if dim M is odd. In addition, we show that variationally trivial Lagrangians are characterized by the de Rham cohomology of the base manifold M and the characteristic classes of P of arbitrary degree.
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