Massless little-group generators
= Massless little-group generators
{title2=$N_1=K_1-J_2,\quad N_2=K_2+J_1$}
For a standard null momentum $(E,0,0,E)$ in signature $(+---)$, define $K_i=M^{0i}$ and $J_i=\epsilon_{ijk}M^{jk}/2$. The stabilizing generators are $J_3,N_1,N_2$. The <Poincare algebra> gives $[J_3,N_1]=iN_2$, $[J_3,N_2]=-iN_1$ and $[N_1,N_2]=0$, the Lie algebra of planar Euclidean motions. Evaluating the <Pauli-Lubanski pseudovector> gives $W^2=-E^2(N_1^2+N_2^2)$.