Quantum Theory of Elementary Particles

Abstract

Quantum numbers which may possibly be identified with strangeness $S$, baryon number $B$, and isospin $I$ are found to be natural consequences of the generalized field theory of a spinning particle developed in earlier papers, the theory requiring that $S+2I+2J$ is even, as observed. The generalized Dirac equation for fermions leads to the correct values of $B$, $S$, $I_3$, and $J$, and approximately the correct masses for the states $n$, $p$, ${\Xi }^0$, ${\Xi }^{-}$, ${N_{13}}^{*+}$, ${N_{13}}^{*0\mathrm{}}$, the lowest known states of $I=\frac{1}{2}$, $J=\frac{1}{2}, or \frac{3}{2}$. The generalized Dirac equation for bosons similarly describes these quantities for the $K$ and $K^{*}$ mesons. The generalized Kemmer equation for fermions yields the correct values of $B$, $S$, $I_3$, $J$, and the masses for the ${\Lambda }^0$, ${Y_0}^{*}$, and ${Y_{03}}^{*}$ if the spin of the ${Y_0}^{*}$ is ½, and the generalized Kemmer equation for bosons similarly leads to the correct masses, spins, and isospins for the $S=0\mathrm{}$ states $\phi$, $f$, $\omega$, $\eta$, $\rho$, and predicts $I=1\mathrm{}$, $S=0\mathrm{}$ states at 1-BeV spin 1 (${\chi }_1$?), 1.24-BeV spin $2(B?)\mathrm{}$, 450-MeV spin $0(\zeta ?)$, and $I=0\mathrm{}$ states at 965 MeV (spin 1) and 926 MeV (spin 0). The only arbitrariness in the theory lies in the choice of the two mass parameters for each equation, and in the choice of which combination of two independently conserved currents allowed by each equation is identified with the electric current. The theory satisfies a correspondence principle with the classical relativistic equation of motion of a symmetric top, and yields a prescription for describing states of higher quantum numbers. It then predicts the spin of the ${Y_0}^{**}$ state as $\frac{5}{2}$, correctly describes the spin and mass of the ${N_{15}}^{*}$ state, predicts a series of $N^{*}$ states 166 MeV apart of progressively increasing spin, and describes other states, the properties of which have not yet been investigated.