# Probability a photon will couple with an electron

1. Jan 11, 2011

### Epistimonas

Hello, I am new to these forums and this is my first post.

Anyways, I am trying to come up with a formula of the probability amplitude of an electron-photon coupling; more specifically, a photon colliding with an electron. I used Q.E.D. by Richard Feynman as a basis for the formula, using the simplistic Feynman diagrams and the basic formulas he describes.

The formula is based on an electron starting at an arbitrary point, 1, moving through space-time to an arbitrary point, 2, coupling with a photon, then continuing off in another direction to an arbitrary point 3. Feynman made it sound ridiculously easy to calculate probability amplitudes for such events, however, he used an imaginary spin-0 electron to simplify it. A real electron obviously takes every path connecting the two points and the probability amplitude that it will go from point 1 to 2 is:

E(1 to 2) = P(1 to 2) + P(1 to 3)*n^2*P(3 to 2) + P(1 to 4)*n^2*P(4 to 5)*n^2*P(5 to 2) + .... for all intermediate points

Where n is a number that makes the calculation agree with experiment and is the amplitude for each stop.

Can someone explain the basics of how I would write a formula that includes all intermediate terms? What would they be? When would they stop? Would it have to be represented by a definite integral with an upper limit of infinity?