  If the conventional Maxwell--Lorentz formulation of classical electrodynamics
is adopted in a flat spacetime of arbitrary odd dimension, then the retarded
vector potential $A^\mu$ generated by a point charge turns out to be pure
gauge, $A^\mu=\partial^\mu\chi$. By Gauss' law, the charge shows up as zero.
The classical electromagnetic coupling is thus missing from odd-dimensional
worlds. If the action is augmented by the addition of the Chern--Simons term,
then the classical interaction picture in the three-dimensional world becomes
nontrivial.
