Feynman diagram

A Feynman diagram is a schematic representation of an interaction between particles. Although they are graphical tools, the components are defined in such a way as to represent fully rigorous calculations and are therefore reliable ways of describing interactions. They are used for both particle scattering and particle decay.

For example, the electromagnetic attraction of an electron and a positron can be represented by the diagram

which corresponds to the process

in which the attraction is mediated by the exchange of a Photon $\gamma$.

Components#

Each diagram is divided in three sections:

1. The beginning of the time axis represents the initial state of the process.
2. The center of the time axis shows the interaction.
3. The end of the time axis shows the final state of the process.

How each of these are drawn is highly codified.

The motion of the particles follows a straight line with an arrow on it. The arrow is forward in time for particles and backwards for antiparticles, echoing the fact that antiparticles can, at least mathematically, be interpreted as moving backwards in time.

The interaction is drawn in one of two ways:

• electromagnetic interaction (Photon) uses a wavy line;
• weak interaction (W and Z bosons) also uses a wavy line¹;
• strong interaction (gluon) uses a coiled line.

Gravity is not understood at a particle level, so there is no definition for it.

The point at which the interaction begins and ends is shown with a filled circle and is called a vertex. The size of the vertex circle should be proportional to the square root of the coupling constant of the interaction.

Despite having a clear length on the time axis, the interaction is too brief for the force carrier to be perceivable. Force carriers in Feynman diagrams are always virtual particles and the visual length of the interaction line should not be assumed to have any meaning.

The time axis should always be drawn explicitly. This is especially true since keeping the time axis horizontal or vertical are both common options. Moreover, it's possible to draw diagrams that show processes in other variables, though time is the most common.

Properties#

Feynman diagrams are drawings of actual calculations. As such, they hold all the properties of the math involved, namely:

• At each vertex, all quantum numbers are conserved. They must also be identical to those of the force carrier.
• The exchange particle is inversely proportional to the square of the transferred momentum.
• The Probability of interaction and the cross section are proportional to the square of the amplitude, represented by the diagram: $\text{Prob}\propto\sigma \propto |\ \ \rangle\!\!\sim\sim\!\!\langle\ \ |^{2}$.