  Nonlinear electrodynamics, QED included, is considered against the
Lorentz-noninvariant external field background, treated as an anisotropic
medium. Hamiltonian formalism is applied to electromagnetic excitations over
the background, and entities of electrodynamics of media, such as field
inductions and intensities, are made sense of in terms of canonical variables.
Both conserved and nonconserved generators of space-time translations and
rotations are defined on the phase space, and their Hamiltonian equations of
motion and Dirac bracket relations, different from the Poincar\'e algebra, are
established. Nonsymmetric, but--in return--gauge-invariant, energy-momentum
tensor suggests a canonical momentum density other than the Poynting vector. A
photon magnetic moment is found to govern the evolution of the photon angular
momentum. It is determined by the antisymmetric part of the energy-momentum
tensor.
