Self-duality, helicity conservation, and normal ordering in nonlinear QED

We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree-level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules derived from a generalized normal ordered Lagrangian, we discuss the interrelation of the above two properties of the theory also at higher loops. As an illustration we present two explicit examples; namely we find the generalized normal ordered Lagrangian for the Born-Infeld theory and derive a semiclosed expression for the Lagrangian of the Bossard-Nicolai model (in terms of the weak field expansion with explicitly known coefficients) from its normal ordered form.