Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 304 / 4 / b / Solution

Writing the source interaction as $\mathrm{Tr}(J^{\mu }{A}_{\mu })$, gauge invariance requires the matrix current to transform in the Adjoint representation,The fermion bilinear with this transformation law isup to a convention-dependent overall coupling or generator normalization. It is the Noether current that appears when the free derivative is replaced by $D_{\mu }={\partial }_{\mu }-ig{A}_{\mu }$.