  The recent PVLAS experiment observed the rotation of polarization and the
ellipticity when a linearly polarized laser beam passes through a transverse
magnetic field. The phenomenon cannot be explained in the conventional QED. We
attempt to accommodate the result by employing an effective theory for the
electromagnetic field alone. No new particles with a mass of order the laser
frequency or below are assumed. To quartic terms in the field strength, a
parity-violating term appears besides the two ordinary terms. The rotation of
polarization and ellipticity are computed for parity asymmetric and symmetric
experimental set-ups. While rotation occurs in an ideal asymmetric case and has
the same magnitude as the ellipticity, it disappears in a symmetric set-up like
PVLAS. This would mean that we have to appeal to some low-mass new particles
with nontrivial interactions with photons to understand the PVLAS result.
