Bound States and Bootstraps in Field Theory

Abstract

We present a general, model-independent theory of composite particles. Starting from a general local Lagrangian containing an elementary particle, we show how this particle becomes composite (in a precisely defined sense) as its wave-function renormalization constant tends to zero. As this limit is taken, the usual dynamical type of field equation changes its form. We show that the Green's functions of the theory still possess the usual physical interpretation in the limit; in particular, for renormalizable theories, if a certain coupling constant does not tend to zero, the "composite" propagator possesses a pole at the composite mass and with nonzero residue. We show that the operator form of the Green's-function equations describing the composite particle can be manipulated by natural approximations to explain a wide variety of known modeldependent results on composite particles, and in particular to obtain all the usual types of bootstrap equations. We present a preliminary classification of the operator equations, showing that many of them cannot possess physically meaningful solutions. Our results agree qualitatively with earlier, heuristic discussions. Finally we make some remarks about the possibility of "bootstrapped symmetry schemes."