Local Conservation Laws in a Nonlinear Electrodynamics

By using a generalization of the Lie–Poisson brackets for dual Maxwell and Born–Infeld field strength tensors, we construct gauge invariant axial-vector conserved currents Heisenberg–Euler nonlinear electrodynamics in 4-dimensional Minkowski space-time. The infinite hierarchies given by Lie generally covariant vector axial are established. These upon action gravitational fields, but conservation is broken Einstein–Cartan theory (over Riemann–Cartan space-time). only (3 + 1)-dimensional