Composite-operator effective-action considerations on bound states and correspondingS-matrix elements

Abstract

The exact Bethe-Salpeter equation, the $S$ matrix for bound states, and related Green's functions are treated within the composite-field effective-action formalism. Comparison of two alternative composite effective potentials is made and we conclude that the physical consequences of the two appear to be the same, at least as applied to the Abelian or Abelianized (QCD in lowest order $\frac{1}{N}$) gauge-field-fermion systems. The effective actions themselves are different both on and off shell.