In $\phi^4$ theory with the $\lambda \phi^4 / 4!$ interaction term gives rise to “tadpole” diagrams like this:
If I have a standard QED interaction with $e \bar\psi \gamma^\mu \psi A_\mu$, can I also have tadpole diagrams like this one?
In the $\phi^4$ case the propagator connects to the same vertex twice and therefore $\phi^2$ is used up. In the QED case I am not sure if the $\bar\psi$ and $\psi$ can connect to the same vertex and propagators. I have not seen any of these one-photon fermion loops in my QFT class. Since it is possible in $\phi^4$, I was wondering if the same is possible in QED.
(The diagrams are made with tikz-feynman.)