In theoretical physics, the Coleman-Mandula theorem, named after Sidney Coleman and Jeffrey Mandula, is a no-go theorem that states that the only conserved quantities except for the generators of the Poincare group in a remotely realistic theory must always be Lorentz scalars.

In other words, every quantum field theory that has some non-trivial interactions may have a symmetry group which is always a direct product of the Poincare group and an internal group if there is a mass gap: no mixing between these two is possible. If there is no mass gap, it could be a direct product of the conformal group with an internal group.

Supersymmetry may be considered the only possible "loophole" of the theorem because it contains additional generators (supercharges) that are not scalars but rather spinors. This loophole is possible because supersymmetry is a Lie supergroup, not a Lie group.