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

I n any quantum field theory of mat ter , in part icular in quarkand subquark models, bound states have to be treated. I n coupling theories corresponding bound state equations are derived b y the Gel l -Mann-Low procedure f rom the Greenfunction hierarchy. D u e to certain presuppositions neither the derivation of such generalized Bethe-Salpeter equations nor the normal izat ion of their amplitudes are selfconsistent. I n 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 w i t h boson fusion f rom fermions, which is described b y a nonlinear spinorfield equation w i t h higher order derivatives. Besides the removal of infinities, in coupling theories renormalizat ion ma in ly means the introduction of dressed field operators which allow a biunique map between field operators and particles. For composite particles renormalization means the dressing of the composite systems which must allow the unique identification of dressed composite part icle states independently of the interactions which can take place w i t h other composite systems, i .e . this is in principle the same program as in coupling theories b u t w i t h the t reatment of dressed composite particles instead of dressed field operators. The program is performed for the reaction equations mentioned above.