  The dynamics in QED in a strong constant magnetic field and its connection
with the noncommutative QED are studied. It is shown that in the regime with
the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion
determinant is transformed into the noncommutative $U(1)_{nc}$ gauge symmetry.
In this regime, the effective action is intimately connected with that in
noncommutative QED and the original U(1) gauge Ward identities are broken (the
LLL anomaly). On the other hand, it is shown that although a contribution of
each of an infinite number of higher Landau levels is suppressed in an infrared
region, their cumulative contribution is not (a nondecoupling phenomenon). This
leads to a restoration of the original U(1) gauge symmetry in the infrared
dynamics. The physics underlying this phenomenon reflects the important role of
a boundary dynamics at spatial infinity in this problem.
