Double-logarithmic nonlinear electrodynamics
A new model of nonlinear electrodynamics named as \emph{"double-logarithmic"} is introduced and investigated. The theory carries one dimensionful parameter of the $\beta$ as Born-Infeld electrodynamics. It is shown that the dual symmetry and dilatation (scale) symmetry are broken in the proposed model. The electric field of a point-like charge is derived for this model and it becomes non-singular at the origin and by use of this electric field the static electric energy of a point like charge is calculated. In the presence of an external magnetic field the theory shows the phenomenon known as vacuum birefringence. The refraction index of two polarizations, parallel and perpendicular to the external magnetic induction field are calculated. The canonical and symmetrical Belinfante energy-momentum tensors are obtained. Using the causality and unitarity principles the regions where the theory becomes causal and unitary are found.