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

Abstract

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 $\frac{N}{D}$ formalism, may be identified with the requirements that the strong-vertex ($Z_v$) and wave-function ($Z_3$) 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 $Z_v=0\mathrm{}$, and by reducing the second vertex equation to the statement $Z_3=0\mathrm{}$ 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.