Moller u-channel

Perturbative order$\alpha$ (tree level)
Topologyu-channel
Symmetry factorCounts overcounting in the perturbation series. If a diagram has internal symmetries—ways to relabel internal lines and get the same diagram back—the symmetry factor divides that out. In QED, most diagrams have S=1 because fermion arrows break the symmetry between internal lines.1.0
Divergence finite
Gauge invariant aloneNo

Contributes to

Moller scattering

Exchange diagram where the outgoing electrons are swapped relative to the t-channel.

The computational chain

From diagram to number—every step of the amplitude calculation.

The diagram
The two outgoing electrons are swapped relative to the t-channel: electron 1 scatters into the $p_2'$ state and electron 2 into the $p_1'$ state. The virtual photon carries momentum $k = p_1 - p_2'$ with $k^2 = u$.
Feynman rules expression
$$i\mathcal{M}_u = \frac{ie^2}{u}\left[\bar{u}(p_2')\gamma^\mu u(p_1)\right]\left[\bar{u}(p_1')\gamma_\mu u(p_2)\right]$$
Each electron line contributes a current $\bar{u}\gamma^\mu u$, connected by the photon propagator $-ig_{\mu\nu}/u$. This is the t-channel expression with $p_1' \leftrightarrow p_2'$, which maps $t \to u$ in the propagator denominator.
Squared amplitude (u-channel alone)
$$\overline{|\mathcal{M}_u|^2} = \frac{2e^4(s^2 + t^2)}{u^2}$$
The traces factorize into two-current form, with each trace evaluated by the standard four-gamma identity.

Related diagrams

Exchange Symmetry