Dynamical Groups and Mass Formula

Abstract

The homogeneous Lorentz group and the 4+1 de Sitter group are interpreted as the dynamical groups of a nonrelativistic and a relativistic "rotator," respectively. In an irreducible representation of the latter group we obtain for certain states the mass formula $m^2={m_0}^2+{\lambda }^{2}j(j+1\mathrm{})\mathrm{}$. The contraction of the dynamical groups [Euclidean group in three dimensions and Poincaré group, respectively] destroys the energy or mass spectrum and can be associated with the limit $\hslash \to 0$. The model of an elementary particle as a de Sitter "rotator" is discussed.