  We propose the bosonization of a many-body fermion theory in D spatial
dimensions through a noncommutative field theory on a (2D-1)-dimensional space.
This theory leads to a chiral current algebra over the noncommutative space and
reproduces the correct perturbative Hilbert space and excitation energies for
the fermions. The validity of the method is demonstrated by bosonizing a
two-dimensional gas of fermions in a harmonic trap.
