Since momentum commutes with the supercharge, part iv gives
$$
[C_{\mu\nu},Q_\alpha]
=[B_\mu,Q_\alpha]P_\nu-[B_\nu,Q_\alpha]P_\mu
=-\frac12(P_\mu P_\nu-P_\nu P_\mu)Q_\alpha=0.
$$
Therefore
$$
\boxed{[C_{\mu\nu},Q_\alpha]=0}.
$$
Hermitian conjugation also gives $[C_{\mu\nu},\bar Q_{\dot\alpha}]=0$.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-307/3/v/solution