  I show that there exist twelve independent Dirac equations for spin 1/2
fermions. The Dirac fields that satisfy these equations can be grouped into six
pairs according to the way they transform under continuous space-time
transformations. These six pairs of Dirac equations correspond to the three
quark generations and the three lepton generations. The charged V-A currents
can be formed only from fields of the same pair. This property of the Dirac
fields implies that a quark or lepton may be transformed only into its partner
of the same generation via the charged-current weak interaction. According to
the properties of the charged-current weak interaction, I conclude that
different elementary fermion fields must satisfy different Dirac equations, and
there may not be more than twelve flavors of elementary fermions that are
already known.
