On the Derivation of Propagator and Bound State Equations and S-Matrix Elements for Composite States

Abstract

Since the work of Cornwall, Jackiw and Tomboulis^l (CJT) on the effective action formalism for composite field operators, emphasis has been placed on its application to the problem of dynamical symmetry breaking, which utilizes the corresponding effective potential. Specifically, the stability of the solutions to the Schwinger-Dyson equation has been regarded as the key issue. Considerably less attention has been given to the possibility of deriving from the composite operator effective action the exact Bethe-Salpeter equations in a general way and to establishing from it the connection to the S-matrix for purely bound-state processes. These properties are of special physical significance for confining theories like quantum chromodynamics (QCD) and we wish to take up these issues in this work.