  Quantum electrodynamics (QED) in a strong constant magnetic field is
investigated from the viewpoint of its connection with noncommutative QED. It
turns out that within the lowest Landau level (LLL) approximation the 1-loop
contribution of fermions provides an effective action with the noncommutative
U(1)_{NC} gauge symmetry. As a result, the Ward-Takahashi identities connected
with the initial U(1) gauge symmetry are broken down in the LLL approximation.
On the other hand, it is shown that the sum over the infinite number of the
higher Landau levels (HLL's) is relevant despite the fact that each
contribution of the HLL is suppressed. Owing to this nondecoupling phenomenon
the transversality is restored in the whole effective action. The kinematic
region where the LLL contribution is dominant is also discussed.
