Representation of SUSY Algebra

  • Thread starter karlzr
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I have some questions about representations of SUSY algebra.
(1) Take ##N=1## as an example. Massive supermultiplet can be constructed in this way:
$$|\Omega>\\
Q_1^\dagger|\Omega>, Q_2^\dagger|\Omega>\\
Q_1^\dagger Q_2^\dagger|\Omega>$$ I understand the z-components ##s_z## of the last state and the first state are the same, but why do they also have the same total spin ##s##?

(2)How do we get to know whether the fermions are Weyl or majorana? For instance ##N=2## hypermultiplet
$$|\Omega_{-\frac{1}{2}}>: \chi_\alpha\\
Q^\dagger|\Omega_{-\frac{1}{2}}>: \phi\\
Q^\dagger Q^\dagger |\Omega_{-\frac{1}{2}}>: \psi^{\dagger \dot{\alpha}}$$ Is this representation CPT invariant? if so, I guess ##\chi## or ##\psi## should be majorana
Or we might need to supplement the states with their CPT conjugates when the two fermion fields are weyl?
 

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