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 Summary
 This isn’t homework, I’m self taught. Pardon me for using pictures instead of typing out equations, I have no clue how to do that. So please don’t downvote this for that :) I’m just really desperate to learn this.
So I’m trying to compute the probability amplitude of an electron with momentum p1 and a positron with momentum p2 annihilating into a photons with momenta q1 and q2.
My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? I wouldn’t mind a stepbystep with minimal assumption similar to the pictures I posted. Any help would be greatly appreciated. Again I’m sorry about the pictures, but I really am unsure how to type out the equations but I hope and assume my writing is legible enough.
What I have so far
My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? I wouldn’t mind a stepbystep with minimal assumption similar to the pictures I posted. Any help would be greatly appreciated. Again I’m sorry about the pictures, but I really am unsure how to type out the equations but I hope and assume my writing is legible enough.
What I have so far
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