Non-local quantum field theory from doubly special relativity

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. In this paper (arXiv:2403.18772) 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.