Quarks: Currents and constituents

An attempt is made to clarify the relation between current quarks and constituent quarks. Assuming that the two are related by a unitary transformation, we outline the properties of this transformation and, in the process, discover a new U(6) × U(6) × O(3) classification algebra for the hadrons. An example of this transformation is constructed in the lightlikeplane formulation of the free-quark model, where the transformation is found to be essentially unique and is just the operator solution to the problem of saturating chiral SU(3) × SU(3). Using the algebraic structure of the free-quark model phenomenologically, matrix elements of currents between different hadrons are related. This abstraction of free-quark algebraic properties works fairly well for the axial-charge and magnetic-moment operators, although it fails for bilocal operators. Nevertheless, we obtain many successful approximate relations between matrix elements of currents, not the least of which is the recovery of the ratio $\frac{{\mu }_T\left(\mathrm{proton}\right)}{{\mu }_T\left(\mathrm{neutron}\right)}=-\frac{3}{2}$.