Elementary question on Moller Scattering Feynman diagrams

[HJ Farnsworth]

Greetings,

I think this will be a very quick thread. I am new to using Feynman diagrams, and have run into something that I find puzzling. The lowest-order Coulomb interaction Feynman diagram is (image from Wikipedia Moller Scattering article):

http://upload.wikimedia.org/wikipedia/en/c/cd/MollerScattering-t.svg


Let's say that we are in a frame where both electrons are initially at rest. Then, it seems to me that because energy and momentum must be conserved between the beginning and end of the diagram, the two electrons must remain at rest after the interaction shown in the diagram above. So, effectively, two electons at rest near each other exchange a photon, and then nothing else happens.

But obviously, two electrons near each other will repel each other, so my question is: how does the phenomenon of two electrons at rest eventually repelling each other actually get represented via a Feynman diagram (or, alternatively, what naive mistake in my interpretation am I making)?

Thanks for any help that you can give.

-HJ Farnsworth

 

[mfb]

Scattering descriptions don't work properly for particles at rest. The assumption that the initial and final states are without interactions fails. You can treat the system similar to bound states, see this thread for example. Solve the "classical" problem first and then calculate corrections to that.

 

[andrien]

Let's say that we are in a frame where both electrons are initially at rest.

you can not find a frame in which both electron is at rest.feynman diagram is used to calculate amplitude.