# Coleman-Mandula theorem The Coleman-Mandula theorem states that in a theory with massive particles and scattering in more than 1+1 dimensions, the only possible conserved quantities that transform as tensors under the Lorentz group are: $P_\mu, M_{\mu\nu},$and scalar symmetries charges $Q_i$ that commute with them. ## Ways to get around the no-go theorem - 1+1 dimension - extended charged objects - massless particles (allows [[0028 Conformal symmetry|conformal symmetry]]) - spinorial indices (allows [[0359 Supersymmetry|SUSY]]) - symmetries not of the $S$-matrix (SSB) ## Refs - original: - [[1967#Coleman, Mandula]] - extension to SUSY: - [[1975#Haag, Lopuszanski, Sohnius]] - extension to CFT: - [[2011#Maldacena, Zhiboedov]]