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Coleman–Mandula theorem : ウィキペディア英語版
Coleman–Mandula theorem
The Coleman–Mandula theorem, named after Sidney Coleman and Jeffrey Mandula, is a no-go theorem in theoretical physics. It states that "space-time and internal symmetries cannot be combined in any but a trivial way".〔; Jeffrey E. Mandula (2015). ( "Coleman-Mandula theorem" ) ''Scholarpedia'' 10(2):7476. 〕 Since "realistic" theories contain a mass gap, the only conserved quantities, apart from the generators of the Poincaré group, must be Lorentz scalars.
==Description==
Every quantum field theory satisfying the assumptions, (1) Below any mass M, there are only finite number of particle types (2) Any two-particle state undergoes some reaction at almost all energies (3) The amplitude for elastic two body scattering are analytic functions of scattering angle at almost all energies, and 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."〔(Valuing Negativity | Cosmic Variance )〕〔


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