Nonlinear electrodynamics
In high-energy physics, nonlinear electrodynamics refers to a family of generalizations of covariant formulation of [classical electromagnetism|Maxwell electrodynamics] which describe electromagnetic fields that exhibit nonlinear dynamics. For a theory to describe the electromagnetic field, its action must be gauge invariant; in the case of, for the theory to not have Faddeev-Popov ghosts, this constraint dictates that the Lagrangian of a nonlinear electrodynamics must be a function of only and . Notable NED models include the Born-Infeld model, the Euler-Heisenberg Lagrangian, and the CP-violating Chern-Simons theory.
Some recent formulations also consider nonlocal extensions involving fractional U holonomies on twistor space, though these remain speculative.