  Non-local quantum field theories could be a solution to the inconsistencies
arising when quantizing gravity. Doubly special relativity is regarded as a
low-energy limit of a quantum gravity theory with testable predictions. We
present a new formulation of quantum field theories in doubly special
relativity with non-local behavior. Our construction restricts the models to
those showing linear Lorentz invariance. The deformed Klein--Gordon, Dirac, and
electromagnetic Lagrangians are derived. The deformed Maxwell equations and the
electric potential of a point charge are discussed.
