%0 Journal Article
%A Castrillón López, Marco
%A Muñoz Masqué, Jaime
%A Ratiu, T.
%T Gauge invariance and variational trivial problems on the bundle of connections.
%D 2003
%@ 0926-2245
%U https://hdl.handle.net/20.500.14352/50861
%X 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 dimM is even and zero if dimM 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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