Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 305 / 1 / d / Solution

The quantum electrodynamics interaction is ${\mathcal{L}}_{\mathrm{int}}=-e{j}^{\mu }{A}_{\mu }$, where the Dirac electromagnetic current is $j^{\mu }=\bar{\psi }{\gamma }^{\mu }\psi$. Under parity symmetry in quantum field theory,Invariance of the interaction therefore requires the electromagnetic four-potential to transform as the same Lorentz four-vector:so $A^0$ is parity even and $\mathbf{A}$ is parity odd. Under charge conjugation, the current is odd, $j^{\mu }\mapsto -j^{\mu }$, so invariance requires