  A novel method is developed to derive the original Dirac equation and
demonstrate that it is the only Poincare invariant dynamical equation for
4-component spinor wavefunctions. New Poincare invariant generalized Dirac and
Klein-Gordon equations are also derived. In the non-relativistic limit the
generalized Dirac equation gives the generalized Levy-Leblond equation and the
generalized Pauli-Schrodinger equation. The main difference between the
original and generalized Dirac equations is that the former and latter are
obtained with zero and nonzero phase functions, respectively. Otherwise, both
equations describe free elementary particles with spin 1/2, which have all
other physical properties the same except their masses. The fact that the
generalized Dirac equation describes elementary particles with larger masses is
used to suggest that non-zero phase functions may account for the existence of
three families of elementary particles in the Standard Model. This suggestion
significantly differs from those previously made to account for the three
families of particle physics.
