Non-trivial coupling of internal and space-time symmetries

Previous results which exhibit the impossibility of combining internal and space-time symmetries are reanalysed. Starting with McGlinn's (1964) work, where this trivial coupling appears as a direct product of these symmetries, it is shown that, by suitable generalisations such as the use of the framework of group extensions, and by the introduction of a new quantal observable, i.e. a mass-breaking operator, one can prove the existence of a non-trivial coupling scheme which admits mass splitting for the members of some super-multiplet. This leads to a new classification scheme for elementary particles. Contrary to the conventional classification models, where the choice of the underlying symmetry group does not emerge directly from the comparison of theoretical predictions with the experimental data, our scheme admits the possibility of determining the relevant symmetry from the mass spectrum.