On-shell Lagrangians as total derivatives and the generalized Komar charge

TL;DR

This paper explores how certain Lagrangians that scale homogeneously can be expressed as total derivatives on-shell, providing a universal form that aids in constructing generalized Komar charges.

Contribution

It introduces a method to write homogeneously transforming Lagrangians as universal total derivatives on-shell, enhancing the understanding of conserved charges in field theories.

Findings

Homogeneous Lagrangians can be expressed as total derivatives on-shell.

The universal expression for these derivatives is solution-independent.

Application to generalized Komar charges enhances conserved charge constructions.

Abstract

Lagrangians which transform homogeneously under a global transformation of the fields (a global rescaling, for instance) can be written on-shell as a total derivative which has a universal, solution-independent expression, using a functional version of the Euler theorem for homogeneous functions. We study the uniqueness of this expression and how this result can be used in the construction of generalized Komar charges.