Dynamical Groups and Mass Formula

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={m₀}^2+^2j (j+1). The contraction of the dynamical groups Euclidean group in three dimensions and Poincar\'e group, respectively destroys the energy or mass spectrum and can be associated with the limit 0. The model of an elementary particle as a de Sitter "rotator" is discussed.