Euler-Lagrange equations for functionals defined on Fr\'echet manifolds

TL;DR

This paper extends the Euler-Lagrange equations to functionals on Fréchet manifolds, which are important in physical theories involving infinite-dimensional spaces.

Contribution

It provides a new formulation of variational calculus applicable to Fréchet manifolds, broadening the scope of classical mechanics and field theory.

Findings

Derived Euler-Lagrange equations for Fréchet manifolds.

Applicable to spaces of sections of vector bundles in physics.

Enhances mathematical tools for infinite-dimensional variational problems.

Abstract

We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fr\'echet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.