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

A fully relativistic, four-dimensional field theoretical model for strong interactions is constructed 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'. The new non-associative, cluster algebra is developed and used 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 fireball and clusters no longer appear. (28 refs).