A soluble field theoretical model for strong interactions inspired by the statistical bootstrap

Abstract

We construct a fully relativistic, four-dimensional field theoretical model for strong interactions in which the interaction is described by a bootstrap integral equation instead of a Lagrangian. One of the most prominent features of strong interactions recursive clustering, has been built in by means of a new algebraic operation, called “cluster”. We develop the new, non-associative, cluster algebra and use it to formulate the bootstrap equation, which can be solved explicitly yielding the exponential hadron mass spectrum known from statistical bootstrap and dual models. From the solution of the bootstrap equation for “fireball operators” a non-trivial, unitary S-matrix can be calculated in closed form, in which fireballs and clusters no longer appear. While having much of the flavour of strong interactions, the model suffers from yielding (in its present form) only isotropic final momentum distributions with, however, the typical exponential momentum cut-off known from statistical bootstrap.