Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 301 / 3 / b / Solution

Under charge conjugation, $\varphi \leftrightarrow {\varphi }^{\ast }$ must be accompanied byThen $D_{\mu }\varphi$ is exchanged with $(D_{\mu }\varphi {)}^{\ast }$, while $F_{\mu \nu }\mapsto -F_{\mu \nu }$. The scalar kinetic and mass terms are therefore exchanged with themselves and $F_{\mu \nu }{F}^{\mu \nu }$ is unchanged, proving invariance of scalar quantum electrodynamics.