Bootstraps and the Pion-Nucleon System

Abstract

It has been suggested that all the observable properties of strongly interacting systems can be determined self-consistently if there do not exist any elementary particles in the conventional sense. This conjecture is applied to the nucleon mass and the pion-nucleon coupling constant, which are calculated under the assumption that the nucleon is composite, and that its existence is a consequence of the same forces which produce pion-nucleon resonances. A self-consistent calculation is possible because the nucleon and the $P_{\frac{3}{2}\frac{3}{2}}$ resonance are principally responsible for the forces which produce each other, providing an example of a "bootstrap" or self-supporting mechanism. The $\frac{N}{D}$ method is used for computations. Some ambiguity in the quantitative results due to high-energy processes is unavoidable, but calculations with a large range of "cutoff" values predict the same orders of magnitude as are observed experimentally. It is shown qualitatively that the self-consistent method not only predicts the nucleon and the $P_{\frac{3}{2}\frac{3}{2}}$ resonance, but excludes other combinations which are not observed. This notion is illustrated by consideration of hypothetical interactions between nucleons and scalar mesons and between $\Lambda$ and $\Sigma$ hyperons of negative relative parity.