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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.