Renormalization group and compositeness in quantum-field theory

By making use of the renormalization group technique, we show that the compositeness conditions required for the equivalence of quantum chromodynamics and the corresponding four-fermion theory may be demonstrated for a large class of gauges. It is also pointed out from a study of soluble models that the equivalence in the sense that the wave functions are the same for finite energy does not guarantee the total equivalence of the Yukawa-type theory to the four-fermion theory.