A variational framework for higher order perturbations

Abstract

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a perturbation drags solutions into solutions and the dragged perturbed solutions can be expanded in a series with respect to the flow parameter, hence it contains perturbations at any order. Mechanics is included as a special case. As a simple application, we recover the well-known discussion about stability of geodesics on a sphere $S_2$.

arXiv comment14 pages

References in corpus (3)

• The Hessian and Jacobi Morphisms for Higher Order Calculus of Variations
• Symmetry transformations of extremals and higher conserved quantities: invariant Yang--Mills connections
• The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background