Application of Generalized Field Theory to Baryons

The simplest relativistic wave equations for a particle which in the classical limit possesses moments of inertia about more than one axis are Dirac and Kemmer-Duffin equations containing extra terms which cause these equations to describe a variety of spin states. The classical field theory of such wave equations is developed and the generalized Dirace equation for particles of spin ½ and $\frac{3}{2}$ is examined in detail. It is found that with the choice of two parameters, one of which merely determines the scale, this equation not only correctly describes the spin and charge states of the particles and resonances ${\Xi }^{-}$, ${\Xi }^0$, $n$, $p$, $N^{**}$, $N^{**0\mathrm{}}$; it also yields their masses correct to better than 2%. The ${\Xi }^{-}-{\Xi }^0$ and $n-p$ mass differences have the correct sign but are several times their observed values. Choice of one other parameter to give the correct $n-p$ mass difference would lead to even better agreement with experiment for the other states, but would also lead to proton and neutron isobars lying 20 MeV above the ground state.