Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 3 / d / Solution

In the rest frame $P^{\mu }=(m,0,0,0)$, antisymmetry gives $W_0=0$. Taking ${ϵ}_{0123}=+1$ and $J_3=M^{12}$ givesHenceThe sign of the second eigenvalue reverses if the opposite Levi-Civita convention is chosen.