A fundamental particle model (II)

Abstract

This paper pursues the discussion of a fundamental particle model proposed in a previous paper. The model for baryons and mesons starts from a fundamental non-linear equation of motion for the field operator in the Heisenberg representation, with a formally symmetric self-interaction. Equations of motion are generated for particles and particle interactions from the equation of motion of the field by using the τ-function formalism. The equation of motion of a single baryon is discussed and it is argued that, if one confines the analysis to the mass shells and the asymptotic domain, a solution is found which should be rather accurate. This equation of motion is then completely integrated in momentum space for pseudoscalar, vector and pseudovector self-interaction terms. A new method is discussed for finding the low energy peripheral interaction of two baryons from the fundamental equation, for all three types of self-interaction. The vector and pseudovector types have explicity velocity dependent terms even in the lowest approximation. Possible conflicts between the demands of the low energy interaction of two baryons, and the baryon self-energy problem are discussed. It appears possible that the origin of self-energy lies in a very short range self-interaction. Numerical computations of the baryon self-energy problem are then exhibited for an extensive range of meson mass parameters. Possible cases of self-interaction are discussed which would give the nucleon and Λ-baryon masses, with the basic mass m 0 = 0. In one of these cases it is shown from the numerical results that the ghost mass appearing in the baryon propagator does not satisfy the asymptotic wave equation which the real masses do satisfy. It is further suggested that the leptons and the photon are associated with the notion of saturated compounds in the strong coupling theory. A strong coupling theory would then have the more massive strongly interacting particles, and have the saturated compounds as lighter, weakly interacting particles. A tentative sketch is given of a fundamental theory based on three basic baryons, n, p, Λ in strong self-interaction, in which strongly interacting hyperons and mesons appear as well as weakly interacting leptons and photons.