Noether's theorem in non-local field theories

TL;DR

This paper extends Noether's theorem to non-local and higher-derivative field theories, deriving explicit conserved currents and tensors, and provides an example involving non-local scalar fields with broken symmetries.

Contribution

It introduces explicit formulas for conserved currents in non-local and higher-derivative theories, expanding the applicability of Noether's theorem.

Findings

Explicit conserved currents for non-local theories derived

Analytical expressions for currents in non-local scalar fields with broken symmetries

Demonstration of Noether's theorem extension to non-local and higher-derivative cases

Abstract

Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.