Vacuum polarization in magnetic field

The dispersive properties of free space in the presence of a magnetic field are calculated in the lowest order in the fine-structure constant, but exactly in the field. An integral representation of the corresponding index of refraction is written, exhibiting the dispersive and birefringent properties of the vacuum, with absorption coming in for transverse photon momenta above the pair production threshold. The weak-field limit and the dominant behavior in strong fields are explicitly calculated.