Spinor space and mass formula for hadrons

Abstract

In this note a representation of space-time as a bilinear product of spinors and a suggestion concerning the nature of space-time in the region occupied by an elementary particle are examined. These ideas were put forward by S~Rz (1), who defined the internalsymmetry algebra Ua in terms of differential operators in the spinor variables and then derived the Gell-Nfann-Okubo (2) mass formula for hadrons from the tensor properties of the mass operator of the external (de Sitter) space-time symmetry algebra. The novelty of this approach prompts us to consider its relationship to the way in which this problem has been attempted previously, i.e: by embedding the external and internal symmetry algebras in a larger higher-symmetry or noninvariance algebra Let W~ be a four-component complex spinor, providing a basis for the fourdimensional representation of SUe.e, the group of 4 x 4 complex unimodular matrices satisfying