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## Homework Statement

If the electron and photon were spinless, in the non-relativistic limit we can write the Lagrangian as: $$L=-\frac{1}{2}\phi_e(\Box+m_e^2)\phi_e-\frac{1}{2}A_0\Box A_0+em_eA_0\phi_e\phi_e$$ For Moller scattering $$e^-e^- \to e^-e^- $$ Draw the three tree level diagrams following from the Lagrangian.

## Homework Equations

## The Attempt at a Solution

So the interaction part must couple 2 electrons with a photon. 2 tree level diagrams are normal scattering (like in QED) in t and u channel. What is the 3rd one? Is there another vertex I am missing from the Lagrangian? Thank you!