The perturbation functor in the calculus of variations

Abstract

In the framework of second order Calculus of Variations on jet bundles we show that the operator which determines the “First Variation” is a functor which we call “Perturbation Functor”. This functor allows us to link the Jacobi morphism for the second variation to the first variation of a new Lagrangian. Its naturality properties are discussed. We also show that it permutes with most of the relevant cohomology functors of the Calculus of Variations and with the de Rham’s one.

Keywords

• fibred manifold
• jet space
• first variation
• category
• functor