Past exam of the theoretical physics I course of the University of Cambridge / 2014 / Paper 1 / 5 / a / Solution

For the supplied Lagrangian, variation with respect to ${\varphi }^{\ast }$ usesThus $\square \varphi +2ie{A}^{\mu }{\partial }_{\mu }\varphi +ie({\partial }_{\mu }{A}^{\mu })\varphi +m^2\varphi =f$. In the Lorenz gauge,For real external fields and driving, the conjugate equation has $-2ie{A}^{\mu }{\partial }_{\mu }$ acting on ${\varphi }^{\ast }$. The supplied model has no $e^2{A}^2|\varphi {|}^2$ term; one must not insert such a term from a different minimally coupled Lagrangian.