Field-theoretic formulation of the bootstrap hypothesis

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 conditions.