Some remarks on nonlinear electrodynamics (Q1682324)

Summary: By using the gauge-invariant, but path-dependent, variables formalism, we study both massive Euler-Heisenberg-like and Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit. It is shown that massive Euler-Heisenberg-type electrodynamics displays the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics. As a result, for the case of massive Euler-Heisenbeg-like electrodynamics (Wichmann-Kroll), unexpected features are found. We obtain a new long-range (\(1 / r^3\)-type) correction, apart from a long-range \((1 / r^5\)-type) correction to the Coulomb potential. Furthermore, Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit (to the leading logarithmic order) displays a long-range (\(1 / r^5\)-type) correction to the Coulomb potential. Besides, for their noncommutative versions, the interaction energy is ultraviolet finite.