  The angular dependence of the differential cross section of unpolarized
light-by-light scattering summed over final polarizations is the same in any
low-energy effective theory of quantum electrodynamics and also in Born-Infeld
electrodynamics. In this paper we derive general expressions for
polarization-dependent low-energy scattering amplitudes, including a
hypothetical parity-violating situation. These are evaluated for quantum
electrodynamics with charged scalar or spinor particles, which give strikingly
different polarization effects. Ordinary quantum electrodynamics is found to
exhibit rather intricate polarization patterns for linear polarizations,
whereas supersymmetric quantum electrodynamics and Born-Infeld electrodynamics
give particularly simple forms.
