On Lagrangian and non-Lagrangian conformal-invariant nonlinear electrodynamics

A general approach is presented to describe nonlinear classical Maxwell electrodynamics with conformal symmetry in flat spacetime. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on conformal-invariant functions of the field strengths. This allows a characterization of Lagrangian and non-Lagrangian theories. We obtain a general formula for possible Lagrangian densities in nonlinear conformal-invariant electrodynamics. This generalizes the standard Lagrangian of classical linear electrodynamics so as to preserve the conformal symmetry.