Gauge-invariant variationally trivial problems on T∗M

Abstract

The paper presents some basic facts concerning the formulation of the gauge invariance property of the electromagnetic field in terms of differentiable manifolds. For example, the gauge potentials are identified as differential one-forms on the manifold. The Lagrangian densities invariant under the algebra of the infinitesimal gauge transformations are also disscussed. From the set of these Lagrangians, the class of variationally trivial Lagrangians is interpreted in terms of multivector fields on the ground manifold.