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Quantum electrodynamics (QED) in a strong constant magnetic field isinvestigated from the viewpoint of its connection with noncommutative QED. Itturns out that within the lowest Landau level (LLL) approximation the 1-loopcontribution of fermions provides an effective action with the noncommutativeU(1)_{NC} gauge symmetry. As a result, the Ward-Takahashi identities connectedwith 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 thehigher Landau levels (HLL's) is relevant despite the fact that eachcontribution of the HLL is suppressed. Owing to this nondecoupling phenomenonthe transversality is restored in the whole effective action. The kinematicregion where the LLL contribution is dominant is also discussed.Comment: 11 pages, 2 figures; references added; based on talk given at The  27th Annual Montreal-Rochester-Syracuse-Toronto Conference on High Energy  Physics (MRST 2005), Utica, New York, 16-18 May 200

NONCOMMUTATIVITY VS. TRANSVERSALITY IN QED IN A STRONG MAGNETIC FIELD