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Susy introduction paper superspace

  1. Jan 23, 2008 #1

    I have read in a susy introduction paper that if we call Q the charge which links fermions and bosons, then we have the following anticommutation relation :
    {Q_a, Q_b} = 2 sigma_ab P
    where P is 4-momentum.
    So, is this relation only due to Coleman-Mandula theorem which force the result of the anticommutation relation to be P ? Or is there any other deeper reason ?
    Because it seems this is this relation which explains the building of a superspace.
  2. jcsd
  3. Jan 27, 2008 #2

    Actually Coleman-Mandula says that there cant be any symmetry linked in a nontrivial way with the Poincare-group. The way around is the Haag-Lopuszanski-Sohnius-Theorem (the second name may be misspelled). If you want a proof for this theorem, try Weinberg Vol 3.
    The basic idea is that there are no other operators transforming the way Q_a Q_b has to, so the anticommutator can only be proportional to P.

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