Haag-Łopuszański-Sohnius theorem

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The Haag-Łopuszański-Sohnius theorem of theoretical physics (found in 1975 by Rudolf Haag , Jan Łopuszański and Martin Sohnius ) states that the symmetries of a consistent quantum field theory are not already maximal with a trivial combination of internal symmetry groups and the Poincaré algebra ( Coleman -Mandula theorem ), but only and exclusively with the inclusion of supersymmetry (SUSY).

The decisive way out of the no-go theorem (English) of Coleman and Mandula was to allow not only boson but also fermionic generators . This is how you get the supersymmetry between bosons and fermions . The fermionic generators only change the spin of the particles, all other quantum numbers are not influenced. In particular, the SUSY generators commutate with the four-pulse , but the anti- commutator of two SUSY generators provides a space-time transformation.

literature

  • Rudolf Haag, Jan T. Lopuszanski, Martin Sohnius: All possible generators of supersymmetries of the S-matrix . In: Nuclear Physics B . tape 88 , no. 2 , March 24, 1975, p. 257-274 , doi : 10.1016 / 0550-3213 (75) 90279-5 .