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

TL;DR

This paper proves the equivalence of electric-magnetic duality and helicity conservation in nonlinear electrodynamics, explores their relation at higher loops, and provides explicit examples including Born-Infeld and Bossard-Nicolai models.

Contribution

It establishes a theoretical link between duality and helicity conservation and derives normal ordered Lagrangians for specific nonlinear electrodynamics models.

Findings

Proved the equivalence of duality and helicity conservation at tree level.

Derived normal ordered Lagrangians for Born-Infeld and Bossard-Nicolai models.

Discussed higher-loop relations between duality and helicity conservation.

Abstract

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 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 semi-closed 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.