  Starting from the multi-local Klein-Gordon equations with Lorentz-scalar
squared-mass operator we give a covariant quark representation of the general
composite mesons and baryons with definite Lorentz transformation property. The
phenomenologically observed hadron mass spectra is pointed out to satisfy
possibly the approximate symmetry under the tilde U(4) transformation group
concerning the spinor freedom of light constituent quarks, including the chiral
transformation as a subgroup. This symmetry predicts the existence of new type
of chiral mesons and baryons out of the conventional framework in
non-relativistic quark model: For light q qbar systems, the scalar sigma- and
axial-vector a1-nonets are predicted to exist as relativistic S-wave states
besides the ordinary P-wave state mesons. Two "exotic" JPC=1-+ mesons are
predicted to exist as relativistic P-wave states, which are possibly assigned
as pi1(1400) and pi1(1600). For light quark baryons the extra 56 with positive
parity and the extra 70 with negative parity of the static SU(6) are predicted
to exist as the ground state chiral particles.
