  We obtain a Quantum Electrodynamics in 2+1 dimensions by applying a
Kaluza--Klein type method of dimensional reduction to Quantum Electrodynamics
in 3+1 dimensions rendering the model more realistic to application in
solid-state systems, invariant under translations in one direction. We show
that the model obtained leads to an effective action exhibiting an interesting
phase structure and that the generated Chern--Simons term survives only in the
broken phase.
