Some Equivalent Approaches to the Self-Consistent Bound State of Strongly Interacting Particles

It is shown that the method known as the unsubtracted bootstrap, by which one calculates the mass and residue of a self-consistent bound state of strongly interacting particles in the N/D formalism, may be identified with the requirements that the strong-vertex (Zᵥ) and wave-function (Z₃) renormalization constants of the composite vanish simultaneously. The unsubtracted bootstrap is also shown to be equivalent to the self-consistent bound-state model of Liu by identifying the first vertex equation of that model with Zᵥ=0, and by reducing the second vertex equation to the statement Z₃=0 through the application of a Ward identity. The proof of equivalence is confined to S-wave bound states in the lowest order of self-consistency.