Description and interpretation of the internal symmetries of hadrons as an exchange symmetry

We review previous work on the use of finite groups to describe the internal symmetries of fundamental particles. For low-lying multiplets the representations of Lie groups coincide with these of simple finite groups. In nature, only very low values of the internal quantum numbers for the basic constituents occur. Finite groups lead to the same selection rules for the S-matrix. It is further possible to give a physical interpretation to these finite groups. In a theory based on stable particles (p, e, ν) as constituents, the additive quantum numbers count the number of indestructible constituents, while the symmetries associated with SU(2), SU(3), SU(4),… for the composite hadrons are reduced to the exchange of constituents between the hadrons and equality of the forces in symmetric and antisymmetric states, respectively. All the lowering and raising operators of the symmetry algebras acquire a definite physical meaning. Other consequences are briefly discussed.