Higher-order Cartan symmetries in k-symplectic field theory

TL;DR

This paper explores higher-order Cartan symmetries in k-symplectic Hamiltonian field theories, revealing new conservation laws through generalized Noether theorems beyond traditional symmetries.

Contribution

It introduces a novel class of infinitesimal transformations in k-symplectic field theories that generate conservation laws without being Noether symmetries.

Findings

Identification of higher-order Cartan symmetries in k-symplectic frameworks

Development of a generalized Noether theorem for these symmetries

Discovery of new conservation laws in Hamiltonian field theories

Abstract

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable generalization of the Noether theorem.