Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 1 / c / Solution

Varying $\bar{\psi }$ and $\psi$ independently givesand its adjointwhere $D_{\mu }\bar{\psi }={\partial }_{\mu }\bar{\psi }-ie{A}_{\mu }\bar{\psi }$. Varying $A_{\nu }$ and integrating the Pauli term by parts gives the modified Maxwell equations