Yang-Mills Dynamics as Effective Nonlinear Field Theory of Composite Vector Bosons in Unified Spinorfield Models

Abstract

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preonantipreon scalar boson states and three-preon fermion (and anti-fermion) states was studied in the low energy as well as in the high energy limit, leading to a functional energy representation of an effective Yukawa theory (with high energy form-factors). In this paper the effective dynamics of two-preon composite vector bosons is studied. The weak mapping of the functional energy representation of the spinorfield on to the functional energy representation for the effective vector boson dynamics (with interactions) produces a non-abelian SU (2) local gauge theory (Yang-Mills theory) for a triplet of mass-zero vector bosons in the temporal and Coulomb gauge. This special gauge is enforced by the use of the energy representation and is compatible with the nonlinear Yang-Mills dynamics (and quantization). Apart from the non-abelian Gauss-law all other field laws and constraints directly follow from the mapping procedure. The non-abelian Gauss-law is a consequence of the relativistic invariance of the effective dynamics. PACS 11.10 Field theory PACS 12.10 Unified field theories and models PACS 12.35 Composite models of particles