  We first present a general method for extracting collective variables out of
non-relativistic fermions by extending the gauge theory of collective
coordinates to fermionic systems. We then apply the method to a system of
non-interacting flavored fermions confined in a one-dimensional
flavor-independent potential. In the limit of a large number of particles we
obtain a Lagrangian with the Wess-Zumino-Witten term, which is the well-known
Lagrangian describing the non-Abelian bosonization of chiral fermions on a
circle. The result is universal and does not depend on the details of the
confining potential.
