  We construct a class of Abelian and non-Abelian local gauge theories that
consist only of matter fields of fermions. The Lagrangian is compact and local
without containing an auxiliary vector field nor a subsidiary condition on the
matter fields. Because of the special structure, this Lagrangian can be
extended to non-Abelian gauge symmetry only in the case of SU(2) doublet matter
fields. We carry out explicit dynamical computation in the leading 1/N order to
show that massless spin-one bound states appear with the correct gauge
coupling. Our diagram calculation exposes the dynamical features that cannot be
explored in the formal auxiliary vector-field trick. For instance, it shows
that the s-wave fermion-antifermion interaction alone cannot form the bound
gauge-bosons; the fermion-antifermion pairs must couple to the d-wave state
too. One feature common to our class of Lagrangian is that the Noether current
does not exist. Therefore it evades possible conflict with the no-go theorem of
Weinberg and Witten on formation of the non-Abelian gauge bosons.
