Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 307 / 3 / i

Both terms in $B_{\mu }=W_{\mu }-\frac{1}{4}\bar{Q}{\bar{\sigma }}_{\mu }Q$ commute with momentum. For the first,because the two resulting products of momenta are symmetric in indices contracted with the Levi-Civita symbol. For the second, $[P_{\rho },Q]=[P_{\rho },\bar{Q}]=0$. Therefore