Many-Particle Self-Consistent Model

Abstract

The number and general nature of the self-consistency equations that may arise in a universal bootstrap theory of all strongly interacting particles is discussed. There are more equations than there are variables to be determined, so that it may be possible to bypass some of the divergence difficulties of dispersion theory by making use of a sufficient number of the equations. A general method of attacking the difficulties associated with the many-particle aspect of the problem is discussed. A simple first approximation to the method is applied to a model of four multiplets (pseudoscalar meson, vector meson, baryon ground state, and $j={\frac{3}{2}}^{+}$ baryon excited state), under the assumption that unitary symmetry is approximately valid. It is argued that comparison with experiment of the calculated differences in masses of particles within the same multiplet will provide experimental tests that are meaningful in a low-order approximation to the model. It is shown that if the mass splitting of the baryon octet is assumed to be partly self-generating (i.e., not resulting completely from the mass splitting of the meson multiplets), a nondegenerate solution to the model is most likely if there is a large violation of $R$ invariance.