  Quasi-constant external fields in nonlinear electromagnetism generate a
contribution to the energy-momentum tensor with the form of dark energy. To
provide a thorough understanding of the origin and strength of the effects, we
undertake a complete theoretical and numerical study of the energy-momentum
tensor $T^{\mu\nu}$ for nonlinear electromagnetism. The Euler-Heisenberg
nonlinearity due to quantum fluctuations of spinor and scalar matter fields is
considered and contrasted with the properties of classical nonlinear
Born-Infeld electromagnetism. We also address modifications of charged particle
kinematics by strong background fields.
