On the Derivation of Strong and Electro-weak Interactions in Functional Quantum Theory of the Nonlinear Spinor Field as a Lepton-hadron Model with Quark-confinement

Abstract

In preceding papers the nonlinear spinor field with Heisenberg's dipole regularization was interpreted as a lepton-quark system. In this paper it is demonstrated that this model is able to produce electro-weak as well as strong interactions. For the analytical derivation of these interactions, in Section 1 an improved calculation technique for scattering functionals is developed which corresponds to an interaction representation of relativistic quantum fields with inclusion of bound states, and which is suited for a comparison of its results with conventional field theories, in particular gauge theories. In Section 2 the projection technique from the spinor field into the lepton-quark representation is discussed in detail. The principle which allows the derivation of the various interactions consists in the calculation and incorporation of universal (local) bosons and non-universal (non-local) bosons occuring as bound states of the spinor field, resp., leptonquark fields, into the scattering functional equation. This is performed for local bosons in Section 1 and for non-local bosons in Section 3. In Section 4 it is shown that a subsequent unitarization which corresponds to quark confinement leads to selection rules for lepton-baryon processes which qualitatively correspond to those of grand unification gauge theories. Numerical calculations will be given in subsequent papers