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 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.
Highlights
The electric-magnetic duality is a remarkable on shell symmetry of the equation of motion of the Maxwell theory
An iterative solution of the NGZ condition in terms of one arbitrary function was found in [3] proving at the same time that Maxwell and Born-Infeld (BI) theories are self-dual cases and that there is an infinite class of such theories
The authors proved that this approach appears to be fully equivalent to the one based on the nonlinear twisted self-duality constraint. Both the latter two approaches parametrize the general solution of the NGZ condition in terms of one arbitrary functional which has manifest Uð1Þ rotational symmetry
Summary
The electric-magnetic duality is a remarkable on shell symmetry of the equation of motion of the Maxwell theory. The authors proved that this approach appears to be fully equivalent to the one based on the nonlinear twisted self-duality constraint Both the latter two approaches parametrize the general solution of the NGZ condition in terms of one arbitrary functional which has manifest Uð1Þ rotational symmetry. As a byproduct we find a physical interpretation of the Uð1Þ rotational invariant generating functional which appears in the auxiliary field method of Ivanov and Zupnik (or equivalently in the method of the nonlinear twisted self-duality constraint of Carrasco, Kallosh, and Roiban) in terms of a certain generalization of normal ordering, which simplifies the Feynman rules for perturbative calculation of the S-matrix.
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