Dynamical Theory of Strong Interactions

Abstract

The many-body quantum mechanics of a set of (self-consistent) composite particles is developed for use as the basis for a theory of strong interactions. The theory deals only with physical particles which may in general have an extended spatial structure. It is a bootstrap theory in which physical particles are examined in terms of superpositions of the physical multiparticle states of the theory; no auxillary quantities such as bare particles or fundamental local fields are introduced and no question of renormalization is encountered. Many-particle states are constructed which are (many-) three-momentum eigenstates and whose spatial integrity is assured via cluster-decomposition properties. The present theory is a dynamical theory in the sense that there is a Hamiltonian that respects the extended and composite structure of the particles and which, unlike $S$-matrix theory, allows a system to be studied during the course of its interactions. A drawback of the theory is that it is not manifestly Lorentz-covariant. The present paper deals with the theory in a simplified form in which heavy baryons interact with structureless mesons in the static limit of no baryon recoil. The self-consistent bootstrap dynamics is examined in the lowest order approximation, including some three-body effects. The conventional Born approximation to the scattering amplitude is recovered. The relation between the existence of particles and signs of forces is obtained. In particular the Cutkosky connection between attractive forces and group-theoretic structure is derived.