Non-local quantum field theory from doubly special relativity

Doubly special relativity (DSR) is usually regarded as a low-energy limit of a quantum gravity theory with testable predictions. On the other hand, non-local quantum field theories have been presented as a solution to the inconsistencies arising when quantizing gravity. Here, we present a new formulation of quantum field theories in DSR with non-local behavior. Our construction restricts the models to those showing linear Lorentz invariance. We derive the deformed Klein–Gordon, Dirac, and electromagnetic Lagrangians, as well as the deformed Maxwell equations. We also discuss the electric potential of a point charge. Finally, we analyze the connection between the nonlocality of field theories and DSR.