Weak Mapping and Gauge Fields

Abstract

Atoms and molecules in quantum electrodynamics, and nuclei and mesons in quantum chromodynamics are considered as composite particles built up of elementary leptons, baryons or quarks. Hence the study of the formation of composite particles and the derivation of their corresponding effective dynamics have to be some of the basic aims of abelian and nonabelian gauge theories with respect to their application to atomic and nuclear physics. In the course of the evaluation of these theories numerous investigations were performed concerning the formation of bound states by means of Bethe-Salpeter equations and Schrödinger equations, see Itzykson and Zuber [Itz 80], and the effective dynamics were studied by Fock space methods, e.g. by Meyer [Mey 92], Buchmüller and Dietz [Buch 80] or by path integral evaluation, see e.g. Cahill and Roberts [Cah 85]. Summarizing the results of these investigations one observes the following drawbacks: The bound state calculations are in general not related to a corresponding effective dynamics, the Fock space methods are in contradiction to algebraic representation theory of quantum fields, cf., e.g., Haag [Haag 92], Honegger and Rieckers [Hon 90], and path integrals imply conceptional as well as technical difficulties, in particular with respect to effective dynamics for composite particles, see Rivers [Riv 88]. For a more detailed criticism we refer to Chapters 10 and 11.