force, which is unified with the electromagnetic force at high energy, then we have to add two tree-level diagram for the exchange of a boson. Here we will focus our attention on a strict tree-level QED computation of the cross section, which is rather instructive but maybe not the most accurate description from a physical point-of-view. Before the derivation, we write the 4-momenta as (and for incoming electrons, and for outgoing electrons, and ): The Mandelstam variables are: These Mandelstam variables satisfy the identity: . According to the two diagrams on this page, the matrix element of t-channel is the matrix element of u-channel is So the sum is Therefore, To calculate the unpolarized cross section, we average over initial spins and sum over final spins, with the factor 1/4 (1/2 for each incoming electron): where we have used the relation . We would next calculate the traces. The first term in the braces is Here , and we have used the -matrix identity and that trace of any product of an odd number of is zero. Similarly, the second term is Using the -matrix identities and the identity of Mandelstam variables: , we get the third term Therefore, Substitute in the momentums we have set here, which are Finally we get the unpolarized cross section with and . In the nonrelativistic limit, , In the ultrarelativistic limit, , References External links SLAC E158: Measuring the Electron's WEAK Charge Quantum electrodynamics Scattering theory