Some notable exceptions to the no-go theorem are conformal symmetry and supersymmetry.
It is named after Sidney Coleman and Jeffrey Mandula who proved it in 1967 as the culmination of a series of increasingly generalized no-go theorems investigating how internal symmetries can be combined with spacetime symmetries.
symmetry mixing both flavour and spin, an idea similar to that previously considered in nuclear physics by Eugene Wigner in 1937 for an
At the time it was also an open question whether there existed a symmetry for which particles of different masses could belong to the same multiplet.
[4] It was only later understood that this is instead a consequence of the differing up-, down-, and strange-quark masses which leads to a breakdown of the
[5] The first notable theorem was proved by William McGlinn in 1964,[6] with a subsequent generalization by Lochlainn O'Raifeartaigh in 1965.
[7] These efforts culminated with the most general theorem by Sidney Coleman and Jeffrey Mandula in 1967.
As a result, the theorem played no role in the early development of supersymmetry, which instead emerged in the early 1970s from the study of dual resonance models, which are the precursor to string theory, rather than from any attempts to overcome the no-go theorem.
Any additional spacetime dependent symmetry would overdetermine the amplitudes, making them nonzero only at discrete scattering angles.
Since this conflicts with the assumption of the analyticity of the scattering angles, such additional spacetime dependent symmetries are ruled out.
For a theory with massless particles, the theorem is again evaded by conformal symmetry which can be present in addition to supersymmetry giving a superconformal algebra.
Spacetime dependent internal symmetries are then possible, such as in the massive Thirring model which can admit an infinite tower of conserved charges of ever higher tensorial rank.