Varying the <Yang-Mills theory> field strength and using $\delta A_\mu=D_\mu\alpha$ gives
$$
\delta F_{\mu\nu}
=D_\mu D_\nu\alpha-D_\nu D_\mu\alpha
=-ig[F_{\mu\nu},\alpha]
=ig[\alpha,F_{\mu\nu}].
$$
Thus $F_{\mu\nu}$ transforms covariantly in the adjoint representation.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 305 / 2 / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-305/2/i/solution