Diagrams / Pair annihilation (u-channel)

Pair annihilation (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. 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

Contributes to

Pair annihilation

Crossed version: the two photon emissions are swapped.

The computational chain

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

Crossed annihilation diagram
Same topology as the t-channel but with the two outgoing photons swapped. The virtual electron now carries momentum $p - q_2$ instead of $p - q_1$. Both diagrams must be summed — for identical bosons (photons) the relative sign is positive.

Related diagrams

Crossing Symmetry

Compton u-channel

u-channel

Pair production (u-channel)

u-channel

Exchange Symmetry

Pair annihilation (t-channel)

t-channel