Castrillón López, MarcoKolář, IvanKowalski, OldřichKrupka, DemeterSlovák, Jan2023-06-202023-06-20199980-210-2097-0https://hdl.handle.net/20.500.14352/60805Proceedings of the 7th International Conference (DGA98) held in Brno, August 10–14, 1998.One of the classical problems in the theory of variational calculus is the so-called equivalence problem, which studies whether two Lagrangians L, L′, defined in the 1-jet prolongation of a given bundle, determine the same variational problem. This problem is equivalent to studying the variational triviality of the difference L−L′. On the other hand, the notion of gauge invariance plays a relevant role in the theory of fields, in particular in electromagnetism, in which the structure group is the abelian group U(1). In this framework, the author gives a geometric characterization of the trivial variational problems defined on the bundle of connections of an arbitrary U(1)-principal bundle which are gauge-invariant. It turns out that there is a one-to-one correspondence between the set of these problems and the set of multivector fields χ on the ground manifold M which are divergence-free, that is, Lχv=0, v being a fixed volume form on M.book parthttp://cisne.sim.ucm.es/record=b1962340~S6*spimetadata only access517.9Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias