In dynamical systems, one often encounters actions A ≡ R Ω L(x, v(x))odx which depend only on v, the velocity of the system and on % the distribution of the particles. In this case, it is well–understood that convexity of L(x, ·) is the right notion to study variational problems. In this talk, we consider a weaker notion of convexity which seems appropriate when the action depends on other quantities such as electro–magnetic fields. Thanks to the introduction of a gauge, we will argue why our problem reduces to understanding the relaxation of a functional defined on the set of differential forms (Joint work with B. Dacorogna).