Processes

Each process is defined by its external legs—the particles entering and leaving the interaction region. Select a process to see every diagram that contributes to its amplitude.

$E = 2$

e⁻ e⁻

Electron propagator

$e^- \to e^-$

The electron self-energy $\Sigma(p)$: the sum of all 1PI corrections to the electron propagator. The full dressed...

1 tree 2 1-loop 3 2-loop
γ γ

Photon propagator

$\gamma \to \gamma$

The vacuum polarization tensor $\Pi^{\mu\nu}(q^2)$: the sum of all 1PI corrections to the photon propagator. The...

1 tree 2 1-loop

$E = 3$

e⁻ e⁻ γ

Vertex function

$e^-e^-\gamma$

The dressed vertex $\Gamma^\mu(p,p')$: the sum of all 1PI corrections to the electron-photon vertex. Decomposes into...

1 tree 2 1-loop

$E = 4$

e⁺ e⁻ e⁻ e⁺

Bhabha scattering

$e^+e^- \to e^+e^-$

Elastic scattering of an electron and positron. Two tree-level diagrams contribute: the s-channel (annihilation into...

2 tree 3 1-loop
e⁻ γ e⁻ γ

Compton scattering

$e^-\gamma \to e^-\gamma$

Scattering of a photon off an electron. Two tree-level diagrams (s and u channels) give the Klein-Nishina formula....

2 tree 1 1-loop
γ γ γ γ

Light-by-light scattering

$\gamma\gamma \to \gamma\gamma$

Photon-photon scattering, forbidden classically because Maxwell's equations are linear. In QED it proceeds through a...

1 1-loop
e⁻ e⁻ e⁻ e⁻

Moller scattering

$e^-e^- \to e^-e^-$

Elastic scattering of two electrons. The simplest process involving identical fermions in the initial and final...

2 tree 3 1-loop
e⁺ e⁻ γ γ

Pair annihilation

$e^+e^- \to \gamma\gamma$

Electron-positron annihilation into two photons. Related to Compton scattering by crossing symmetry. The two tree...

2 tree
γ γ e⁻ e⁺

Pair production

$\gamma\gamma \to e^+e^-$

Two photons produce an electron-positron pair. The time-reversed process of pair annihilation. Related by crossing...

2 tree

$E = 5$

e⁺ e⁻ e⁻ e⁺ γ

Bhabha bremsstrahlung

$e^+e^- \to e^+e^-\gamma$

Bhabha scattering with emission of a real photon. The IR divergence of one-loop Bhabha scattering cancels against...
e⁻ γ e⁻ γ γ

Compton bremsstrahlung

$e^-\gamma \to e^-\gamma\gamma$

Compton scattering with emission of an additional photon. The real-emission counterpart to the one-loop Compton amplitude.
e⁺ e⁻ e⁻ e⁻ γ

Inverse trident

$e^+e^-e^- \to e^-\gamma$

A positron annihilates with one of two electrons, producing a photon; the remaining electron exits. Time-reversed...
e⁻ e⁻ e⁻ e⁻ γ

Moller bremsstrahlung

$e^-e^- \to e^-e^-\gamma$

Moller scattering with emission of a real photon. The simplest bremsstrahlung process for electron-electron...
e⁺ e⁻ γ γ γ

Three-photon annihilation

$e^+e^- \to \gamma\gamma\gamma$

Electron-positron annihilation into three photons. For general $e^+e^-$ collisions both spin states contribute. In...
γ γ γ e⁻ e⁺

Three-photon pair production

$\gamma\gamma\gamma \to e^+e^-$

Three photons produce an electron-positron pair. Time-reversed three-photon annihilation.
e⁻ γ e⁻ e⁺ e⁻

Trident pair production

$e^-\gamma \to e^-e^+e^-$

A photon converts to an electron-positron pair in the field of an electron. Called the trident process because three...

$E = 6$

e⁺ e⁻ γ γ γ γ

Annihilation with photon scattering

$e^+e^-\gamma \to \gamma\gamma\gamma$

Electron-positron annihilation in the presence of an incoming photon, producing three outgoing photons.
e⁺ e⁻ γ γ γ γ

Annihilation with photon scattering

$e^+e^-\gamma\gamma \to \gamma\gamma$

An electron-positron pair annihilates in the presence of two additional photons, producing two outgoing photons.
e⁺ e⁻ e⁻ e⁺ γ γ

Bhabha double bremsstrahlung

$e^+e^- \to e^+e^-\gamma\gamma$

Bhabha scattering with emission of two real photons.
e⁺ e⁻ γ e⁻ e⁺ γ

Bhabha with photon scattering

$e^+e^-\gamma \to e^+e^-\gamma$

Electron-positron scattering in the presence of an external photon.
e⁻ γ γ e⁻ γ γ

Double Compton scattering

$e^-\gamma\gamma \to e^-\gamma\gamma$

An electron scatters off two photons, producing two outgoing photons. The natural two-photon generalization of...
e⁺ e⁻ e⁺ e⁻ γ γ

Double pair annihilation

$e^+e^-e^+e^- \to \gamma\gamma$

Two electron-positron pairs annihilate into two photons. Time-reversed double pair production.
γ γ e⁻ e⁺ e⁻ e⁺

Double pair production

$\gamma\gamma \to e^+e^-e^+e^-$

Two photons produce two electron-positron pairs simultaneously. Requires at least 4 vertices at tree level.
e⁻ e⁺ e⁻ e⁻ e⁺ e⁻

Electron-positron-electron scattering

$e^-e^+e^- \to e^-e^+e^-$

Two electrons and a positron scatter. Combines features of Moller (electron exchange) and Bhabha (annihilation...
e⁺ e⁻ γ γ γ γ

Four-photon annihilation

$e^+e^- \to \gamma\gamma\gamma\gamma$

Electron-positron annihilation into four photons. Suppressed by $\alpha^2$ relative to two-photon annihilation. The...
γ γ γ γ e⁻ e⁺

Four-photon pair production

$\gamma\gamma\gamma\gamma \to e^+e^-$

Four photons produce an electron-positron pair. Time-reversed four-photon annihilation. Extremely rare due to the...
e⁻ e⁻ e⁻ e⁻ γ γ

Moller double bremsstrahlung

$e^-e^- \to e^-e^-\gamma\gamma$

Moller scattering with emission of two real photons.
e⁻ e⁻ γ e⁻ e⁻ γ

Moller with photon scattering

$e^-e^-\gamma \to e^-e^-\gamma$

Two electrons scatter in the presence of an external photon.
e⁺ e⁻ e⁻ e⁻ e⁻ e⁻

Pair annihilation to electrons

$e^+e^-e^-e^- \to e^-e^-$

A positron annihilates with one electron from a three-electron initial state, leaving two electrons. Time-reversed...
e⁻ e⁻ e⁻ e⁻ e⁺ e⁻

Pair production by electron

$e^-e^- \to e^-e^-e^+e^-$

An electron-electron collision produces an additional electron-positron pair. The simplest pair production process...
γ γ γ γ γ γ

Six-photon scattering (2→4)

$\gamma\gamma \to \gamma\gamma\gamma\gamma$

Two photons scatter into four photons via a fermion hexagon loop. No tree-level diagrams. Related to six-photon 3→3...
γ γ γ γ γ γ

Six-photon scattering (3→3)

$\gamma\gamma\gamma \to \gamma\gamma\gamma$

Three photons scatter into three photons via a fermion hexagon loop. No tree-level contribution exists — this is an...
e⁻ γ e⁻ γ γ γ

Triple Compton scattering

$e^-\gamma \to e^-\gamma\gamma\gamma$

An electron scatters off a photon and emits three outgoing photons. Higher-order extension of Compton scattering.
e⁻ e⁻ e⁻ e⁻ e⁻ e⁻

Triple electron scattering

$e^-e^-e^- \to e^-e^-e^-$

Three electrons scatter off each other by exchanging virtual photons. Requires at least two photon exchanges at tree...