Generalized ghost-free propagators in nonlocal field theory

In this article, we propose a wider class of symmetries including the Galilean shift symmetry as a subclass. We will show how to construct ghost-free nonlocal actions, consisting of infinite derivative operators, which are invariant under such symmetries, but whose functional form is not simply given by exponentials of entire functions. We also present an iterative method to generate an infinite class of new nonlocal theories whose propagators are ghost-free.