= Solution
For physical finite-spin <one-particle states>, a positive-energy <Poincaré group> representation is labelled by mass and <spin> $(m,j)$ when $m>0$, or mass and <helicity> $(0,h)$ when massless. The individual states also carry their <four-momentum> and a spin projection. For <four-dimensional N=1 supersymmetry>, the irreducible labels become $(m,j_{
m super})$, with $j_{
m super}$ the <superspin>, or $(0,h_{
m super})$, with a chosen <superhelicity> convention. The constituent representation labels are
$$
\boxed{\text{massive: }(m,j),(m,j),(m,j+\tfrac12),(m,j-\tfrac12),}
$$
with the last entry omitted for $j=0$, and
$$
\boxed{\text{massless: }(0,h),(0,h+\tfrac12).}
$$
A required <CPT completion of a supermultiplet> adds the conjugate labels $(0,-h),(0,-h-\tfrac12)$ and conjugates any internal charges.
Back to article page
