  The effective classical/quantum dynamics of a particle constrained on a
closed line embedded in a higher dimensional configuration space is analyzed.
By considering explicit examples it is shown how different reduction mechanisms
produce unequivalent dynamical behaviors. The relation with a formal treatment
of the constraint is discussed. While classically it is always possible to
strictly enforce the constraint by setting to zero the energy stored in the
motion normal to the constraint surface, the quantum description is far more
sensitive to the reduction mechanism. Not only quantum dynamics is plagued by
the usual ambiguities inherent to the quantization procedure, but also in some
cases the constraint's equations do not contain all the necessary information
to reconstruct the effective motion.

High Energy Physics - Theory;Quantum Physics