Null Lagrangians of non-local field theories

TL;DR

This paper characterizes the class of classical smooth Lagrangian densities for non-local field theories, especially relevant in quantum gravity, and discusses implications for non-local Noether theorems.

Contribution

It provides a detailed characterization of null Lagrangians in non-local field theories, enhancing understanding of their equivalence classes and symmetries.

Findings

Characterization of equivalence classes of non-local Lagrangians

Insights into divergence symmetries in non-local theories

Implications for non-local Noether theorem

Abstract

This manuscript provides a characterisation of the equivalence class of classical smooth Lagrangian densities that involve terms depending on two distinct points of the underlying Euclidean base space of the theory. Theories of this type are referred to as non-local field theories, which are of particular interest in the group field theory approach to quantum gravity. The notion of equivalence of Lagrangian densities is set by physical indistinguishability by means of their equations of motion whose derivation is shown briefly. We expect our results to give a more comprehensive view on the non-local Noether theorem regarding divergence symmetries.