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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.