Past exam of the theoretical physics major option course of the University of Oxford / 2016 / 8 / b / Solution

The first-order Dyson series contains $-ig\int d^{4}w{\phi }^{†}\phi \varphi$. For an amputated three-point Feynman diagram, each of the three distinct field types contracts in exactly one way. Writing each external plane wave in momentum space producesThus the momentum-space Feynman rule, with all four-momenta incoming, isAfter stripping the conservation delta factor, it is simply $-ig$. There is no $3!$ combinatorial factor because the interaction has three distinct field slots. The charged lines carry opposite charge-flow orientations and the real heavy line is neutral.