A variational setting for an indefinite Lagrangian with an affine Noether charge

TL;DR

This paper develops a variational framework for indefinite Lagrangians with symmetries, including Lorentz-Finsler cases with timelike Killing vectors, expanding the mathematical tools for analyzing such systems.

Contribution

It introduces a new variational setting accommodating indefinite Lagrangians with affine Noether charges, applicable to Lorentz-Finsler geometries with symmetries.

Findings

Framework for indefinite Lagrangians with symmetries

Includes Lorentz-Finsler Lagrangians with timelike Killing vectors

Enhances mathematical tools for symmetry analysis in physics

Abstract

We introduce a variational setting for the action functional of an autonomous and indefinite Lagrangian on a finite dimensional manifold. Our basic assumption is the existence of an infinitesimal symmetry whose Noether charge is the sum of a one-form and a function. Our setting includes different types of Lorentz-Finsler Lagrangians admitting a timelike Killing vector field.