Dynamical Theory of Hadrons and Leptons

Abstract

This paper is an attempt at a dynamical description of hadrons and leptons by the same wave equation, yielding different mass spectra for each. The wave equation in the six-dimensional representation of $SU(3, 1)$ leads to the following results: (i) mass spectra for spin-½ and spin-$\frac{3}{2}$ leptons (represented by orthogonal states) are obtained in the form of doublets, (ii) the equation can accommodate all the usual $\mathrm{SU}\left(3\right)\mathrm{}$ multiplets of hadrons in the 36 and 216 and higher-dimensional reducible representations of $SU(3, 1)$, and (iii) the internal symmetry is induced by $SU(3, 1)$ parity doubling of the states as well as the $SU(3, 1)$ non-invariance of the wave equation.