  The energy density is computed for a U(2) Chern-Simons theory coupled to a
non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the
assumptions of uniform charge and matter density. When the matter field is a
spinless fermion, we find that this energy is independent of the two
Chern-Simons coupling constants and is minimized when the non-Abelian charge
density is zero. This suggests that there is no spontaneous breaking of the
SU(2) subgroup of the symmetry, at least in this mean-field approximation. For
spin-1/2 fermions, we find self-consistent mean-field states with a small
non-Abelian charge density, which vanishes as the theory of free fermions is
approached.
