I have some questions about representations of SUSY algebra.(adsbygoogle = window.adsbygoogle || []).push({});

(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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# Representation of SUSY Algebra

Can you offer guidance or do you also need help?

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