Spin-Flavour Symmetry and Contractions Towards Classical Space-Time Symmetry

Abstract

A classification scheme of hadrons is proposed on the basis of the division algebra H of quaternions and an appropriate geometry. This scheme suggests strongly to understand flavour symmetry in another manner than from standard symmetry schemes. In our approach, we do not start from `exact' symmetry groups like SU(2) \times SU(2) chiral symmetry and impose various symmetry breaking mechanisms which collide with theorems wellknown from quantum field theory. On the contrary, the approximate symmetry properties of the hadron spectrum at low energies, usually classified by `appropriately' broken compact flavour groups, emerge very naturally as a low energy reduction of the noncompact (dynamical) symmetry group Sl(2,H). This quaternionic approach not only avoids most of the wellknown conceptual problems of Chiral Dynamics but it also allows for a general treatment of relativistic flavour symmetries as well as it yields a direct connection towards classical relativistic symmetry.