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Haag–Lopuszanski–Sohnius theorem
In theoretical physics, the Haag–Lopuszanski–Sohnius theorem shows that the possible symmetries of a consistent 4-dimensional quantum field theory do not only consist of internal symmetries and Poincaré symmetry, but can also include supersymmetry as a nontrivial extension of the Poincaré algebra. This significantly generalized the Coleman–Mandula theorem.
One of the important results is that the fermionic part of the Lie superalgebra has to have spin-1/2 (spin 3/2 or higher are ruled out).
==History==
Prior to the Haag–Lopuszanski–Sohnius theorem, the Coleman–Mandula theorem was the strongest of a series of no-go theorems, stating that the symmetry group of a consistent 4-dimensional quantum field theory is the direct product of the internal symmetry group and the Poincaré group.
In 1975, Rudolf Haag, Jan Łopuszański, and Martin Sohnius published their proof that weakening the assumptions of the Coleman–Mandula theorem by allowing both commuting and anticommuting symmetry generators, there is a nontrivial extension of the Poincaré algebra, namely the supersymmetry algebra.
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