Diagrams / Moller u-channel

Moller u-channel

Perturbative order	$\alpha$ (tree level)
Topology	u-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. Most QED diagrams have S=1; the vacuum polarization bubble has S=1/2 because swapping the two internal fermion lines gives the same diagram.	1.0
Divergence	finite
Gauge invariant alone	No

Contributes to

Moller scattering

Exchange diagram where the outgoing electrons are swapped relative to the t-channel. Required by Fermi statistics: the total amplitude must be antisymmetric under $p_1' \leftrightarrow p_2'$. Enters with a relative minus sign.

The computational chain

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

Exchange diagram

$$i\mathcal{M}_u = \frac{ie^2}{u}\left[\bar{u}(p_2')\gamma^\mu u(p_1)\right]\left[\bar{u}(p_1')\gamma_\mu u(p_2)\right]$$

Same structure as the t-channel but with the outgoing electrons swapped: $p_1' \leftrightarrow p_2'$. Fermi statistics requires this diagram and it enters the total amplitude with a relative minus sign: $\mathcal{M} = \mathcal{M}_t - \mathcal{M}_u$.

Related diagrams

Exchange Symmetry

Moller t-channel

t-channel