New approach to nonlinear electrodynamics: dualities as symmetries of interaction

The duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields is considered/ The field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is presented by a function E depending on thr auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics admit a simple off-shell characterization as symmetry properties of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations od the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. Foe a class of duality-symmetric Lagrangians an alternative representation with the auxiliary scalar field is introduced and new explicit examples of such systems are found