Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 50 / 1 / a / Solution

Positive-energy one-particle Poincaré group representations have labels $(m,s)$ for $m>0$, and $(0,h)$ for finite-helicity massless states; individual massive polarizations add $m_s=-s,\dots ,s$. An $\mathcal{N}=1$ massive supermultiplet is labelled by mass $m$ and superspin $j$, with constituent labelsA massless supermultiplet has constituent labelsA CPT completion of a supermultiplet additionally supplies $(0,-h),(0,-h+\frac{1}{2})$, with conjugated internal charges where applicable. Constituent spins/helicities are the labels here, not counts of polarizations.