The Spinorfield Model

Abstract

The essential symmetry group of relativistic quantum fields is the Poincaré group. All representations of this group can be generated by direct products of elementary spin-1/2 representations, cf. Wigner [Wign 39], Fonda and Ghirardi [Fon 70], Bogoliubov, Logunov and Todorov [Bogo 75], Haag [Haag 92]. Therefore, as this group is fundamental one expects that nature reflects this composition principle, i.e. that spin-1/2 fermions are the basic quantities for any attempt to generate the hierarchy of observable and nonobservable physical particles. This fusion principle originates from de Broglie [Brog 34], [Brog 54]. The mathematical description of spin-1/2 fermions is performed by spinorfields, and as nontrivial interactions are required, the corresponding equations have to be nonlinear spinorfield equations. Thus, at first we will extensively discuss nonlinear spinorfield theory and resulting effective composite particle theories. Later on we will pass to gauge theories, i.e. theories which couple elementary fermions with gauge bosons and which at present are one of the main topics of theoretical research.