Conserved currents from nonlocal constants in relativistic scalar field theories

TL;DR

This paper introduces a novel method to derive locally-conserved currents in relativistic scalar field theories using nonlocal constants, connecting classical mechanics concepts with field theory and recovering standard results.

Contribution

It presents a new approach to obtain nonlocal constants in scalar field theories and derives conserved currents, extending classical mechanics techniques to relativistic fields.

Findings

Derived locally-conserved currents from nonlocal constants.

Recovered standard Noetherian results within the new framework.

Applied methods to nonlinear and dissipative scalar field theories.

Abstract

Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They are a powerful tool to provide first integrals in classical mechanics and, in this respect, a new approach to get nonlocal constants within the framework of lagrangian scalar field theory is introduced. We derive locally-conserved currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein-Gordon theory.