Susy introduction paper superspace

[Barmecides]

Hello,

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.

 

[Eisenhorn]

Greetings,

Actually Coleman-Mandula says that there can't 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.

Eisenhorn.