VERTEX FUNCTIONS AND GENERALIZED NORMAL-ORDERING BY TRIPLE SYSTEMS IN NON-LINEAR SPINOR FIELD MODELS

Abstract

Triple systems, more precisely ternary rings, are closely related to Yang-Baxter symmetries and integrable models. We seek for a possibility to employ triple systems in effective non-linear spinor field theories and explore the nature of q-deformation from an unconventional point of view. Starting with a non-parameter-dependent, that is non-Yang-Baxterian, triple product, we derive at first the BCS interaction. Turning to deformed symmetries leads in some sense to a regular vertex function. The Yang-Baxter matrix is seen to govern the generalized normal-ordering. The connection to the effect of running coupling constants is outlined. Our model shares much features with the recently discussed anisotropic effective local interactions introduced to obtain QCD confinement. A geometrically motivated discussion of the physics behind q-symmetries is given.