  Fierz identities follow from permutations of quark indices and thus determine
which chiral multiplets of baryon fields are Pauli-allowed, and which are not.
In a previous paper we have investigated the Fierz identities of baryon fields
with two light flavours and found that all bilocal fields that can be
constructed from three quarks are Pauli-allowed. That does not mean that all
possible chiral multiplets exist, however: some chiral multiplets do not appear
among structures with a given spin in the local limit, say J = 1/2. One such
chiral multiplet is the [(6,3)+(3,6)], which is necessary for a successful
chiral mixing phenomenology. In the present paper we extend those methods to
three light flavors, i.e. to SU_F(3) symmetry and explicitly construct all
three necessary chiral SU_L(3)*SU_R(3) multiplets, viz. [(6,3)+(3,6)],
[(3,3_bar)+(3_bar,3)] and [(3_bar,3)+(3,3_bar)] that are necessary for a
phenomenologically successful chiral mixing. We complete this analysis by
considering some bi-local baryon fields that are sufficient for the
construction of the "missing" spin 1/2 baryon interpolating fields. Bi-local
baryon fields have definite total angular momentum only in the local limit. The
physical significance of these results lies in the fact that they show that
there is no need for higher Fock space components, such as the (q^4 q_bar), in
the baryon chiral mixing framework, for the purpose of fitting the observed
axial couplings and magnetic moments: all of the sufficient "mirror components"
exist as bi-local fields.
