Field-Theoretic Formulation of the Bootstrap Hypothesis

Abstract

A precise statement of the bootstrap theory in the language of conventional Lagrangian field theory is given. Under no further assumptions than the Mandelstam representation, it is shown that this closed-form theory is equivalent to the more usual $S$-matrix formulation in terms of Regge trajectories. The assumptions of the bootstrap theory are stated in terms of the vanishing of well-defined renormalization constants $Z$. All standard results and approximation methods in the bootstrap theory are shown to follow directly from the $Z=0\mathrm{}$ conditions.