# Calculating Feynman amplitude for closed two loop diagrams

Could someone explain or post a link for how one calculates the Feynman amplitudes for closed two loop diagrams? This is in QED with the same fermion in both loops and a photon connecting them.

• Well what have you tried on your own? – Kyle Kanos Mar 18 '17 at 19:37
• I think I do get how to set up the different factors now, but I am a little unsure how the energy-momentum conservation (delta distributions) should look in diagram A. Say the fermion line on the left has 4-momentum p (going into the vertex from the top) and the photon k (going out of the vertex), should the argument in the delta distribution be (p-k) or (p-p-k)? I know that diagram A will become zero, but am just curious how it would be. – MasterDesperate Mar 19 '17 at 20:41

## 1 Answer

Hint: Multiply the contributions for QED vertices and internal lines. See here: http://bolvan.ph.utexas.edu/~vadim/Classes/2009s.homeworks/QED.pdf

A loop is one internal fermion and one internal antifermion line; here you must involve an integral over $d^4q$ where $q$ is the positron 4-momentum. The integral goes over the product of fermion and antifermion contribution. Imply energy-momentum conservation in delta distribution.

Example: Diagram A has two fermion lines, two antifermion lines, one photon line and two vertices.