Proof of Renormalizability and Derivation of Dynamical Equations for Relativistic Composite Particle Systems and Reactions in Unified Field Models

Abstract

Abstract In any quantum field theory of matter, in particular in quark-and subquark models, bound states have to be treated. In coupling theories corresponding bound state equations are derived by the Gell-Mann-Low procedure from the Greenfunction hierarchy. Due to certain presupposi-tions neither the derivation of such generalized Bethe-Salpeter equations nor the normalization of their amplitudes are selfconsistent. In this paper bound state equations and general reaction equations for composite particles are derived by means of functional techniques which do not rest on such presuppositions. The derivation is performed for a unified lepton-quark model with boson fusion from fermions, which is described by a nonlinear spinorfield equation with higher order derivatives. Besides the removal of infinities, in coupling theories renormalization mainly means the introduction of dressed field operators which allow a biunique map between field opera-tors and particles. For composite particles renormalization means the dressing of the composite systems which must allow the unique identification of dressed composite particle states independently of the interactions which can take place with other composite systems, i.e. this is in principle the same program as in coupling theories but with the treatment of dressed composite particles instead of dressed field operators. The program is performed for the reaction equations mentioned above.