# Representation of SUSY Algebra

1. Feb 1, 2014

### karlzr

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?