Topologies

A topology describes the shape of a Feynman diagram—how vertices and propagators are connected, independent of which particles run through them. The same topology can appear in different processes with different physical content.

Tree-level topologies

Tree (bare)

No loops, no internal structure. A bare propagator or bare vertex — the zeroth-order building block before quantum...

s-channel

Two incoming particles annihilate into a single virtual particle, which then produces two outgoing particles. The...

t-channel

Two particles scatter by exchanging a virtual particle. The exchanged particle carries momentum transfer $k^2 = t =...

u-channel

Like the t-channel but with the outgoing particles crossed: the exchanged particle connects the first incoming to...

One-loop topologies

Box

A closed loop with four vertices forming a quadrilateral. Four internal propagators. The simplest topology for...

Bubble

A single closed loop inserted into a propagator. Two vertices connected by two internal lines running in opposite...

Counterterm

A counterterm insertion — drawn as an X on a propagator or at a vertex. Counterterms arise from rewriting the bare...

Rainbow

A virtual photon emitted and reabsorbed by the same fermion line, arcing over a segment of the propagator like a...

Triangle

A closed loop with three vertices forming a triangle. One vertex connects to an external line (typically a photon);...

Higher-order topologies

Nested

One loop structure completely enclosed inside another. The inner subdiagram sits between two vertices of the outer...

Overlapping

Two loop structures that partially overlap — neither one encloses the other. The defining feature of irreducibly...