Some previous theorems on mass splitting are considered for the case in which there is no mass gap. It is shown that, for a very wide class of definitions of particle masses, including their definitions as eigenvalues (isolated or nonisolated) of the mass operator, any Lie group containing the Poincaré group cannot contain a conventional semisimple spectrum-generating group such as $\mathrm{SU}\left(3\right)\mathrm{}$ or $SL(3, C)$.

• Received 27 December 1967

DOI:https://doi.org/10.1103/PhysRev.171.1698