OK a little information regarding Feynman Rules:
The Feynman Rules for a theory are very simple, but lead to increasingly complicated mathematical expressions as increasingly complicated diagrams are constructed.
The rules for any process are:
- Draw all possible diagrams (up to some number of photons, depending on the accuracy desired). Different time-orderings of a given process are represented by the same diagram.
- Given the initial momentum and energy, define how momentum and energy flow for each line in the diagram. Where each diagram has a closed loop, there is an arbitrary momentum and energy flow around the loop and we must integrate over all possible choices for these quantities. Each intermediate line in the diagram contributes a factor to the amplitude of 1/(E2-p2c2-m2c4) where m is the appropriate mass for the particle type represented by the line. Note that this says that the more "virtual" the particle represented by a line is, the smaller the contribution of the diagram.
- Add the amplitude factors from all possible diagrams to get the total amplitude for the process.
The expected rate for the process can then be calculated -- it is proportional to the absolute value of the total amplitude squared. [Note that this is not the same as the sum of the squares of the absolute values of the individual amplitudes.] For more information on this topic, take a look at the discussion of
quantum interference.