U(12) a new symmetry possibly realizing in hadron spectroscopy

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 U(12) transformation group of light constituent quarks. Here U(12)⊃U(4)DS⊗SU(3)F, and U(4)DS is a homogeneous Lorentz transformation group for Dirac spinors, while SU(3)F is the flavor unitary group. This symmetry predicts the existence of new type of chiral mesons and baryons out of the conventional level classification scheme: typical ones are for light qq̄ system the scalar σ- and axial-vector a1-nonets to be assigned as relativistic S-wave states, while for light-quark–baryon-system the Roper resonance N(1440) (JP=12+) and the Λ(1405) (JP=12−) with comparatively light mass to be assigned as the ground states.