Charge Spectrum of Four-Component Fields with O(4,2) Symmetry

The charge spectrum of a four-component spinor field $\psi \mathrm{}\left(x\right)\mathrm{}$ given by the most general minimal linear parity-conserving current in the O(4,2) algebra of Dirac matrices for a composite spin-½ particle-antiparticle system with an arbitrary number $N$ of mass eigenvalues $m_{\tau }$ ($\tau =1,2,\dots ,N$), where $N\ge 2$, is determined from the structure of the electromagnetic current density postulated recently by Barut, Cordero, and Ghirardi. To within a constant of proportionality, the charge spectrum is found to be fractional, of the form $(e_1,e_2,\dots ,e_N)=\left(\frac{e}{N}\right)\times \mathrm{}\left(\right(N-1\mathrm{}),-1,\dots ,-1)$, which simulates the quark model of Gell-Mann and Zweig for $N=3\mathrm{}$. The implication on the mass spectrum of hadrons is discussed.