Page "Coleman–Mandula theorem" Paragraph 1

Every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincaré group and an internal group if there is a mass gap: no mixing between these two is possible.

As the authors say in the introduction to the 1967 publication, " We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way.