QED Vertex Tee: Alpha Near 1/137

The Vertex Smith has one tool and makes everything with it.

In quantum electrodynamics, the theory of light and charged matter, every process, an electron scattering off another, an atom emitting light, an electron's magnetism, is drawn as a Feynman diagram, and every diagram is assembled from a single building block: a charged particle line meeting a photon line at a point. That point is the vertex on the back of this shirt. Each vertex contributes the factor −ieγ^μ, where e is the elementary charge and γ^μ are the Dirac matrices that carry the electron's spin (the sign depends on convention).

How strongly light and charge couple is measured by the fine-structure constant, α = e²/(4πε₀ħc), with ε₀ the vacuum permittivity, ħ the reduced Planck constant and c the speed of light. All the units cancel, so α is a pure number: CODATA 2022 gives 1/α = 137.035 999 177(21), known to about 0.15 parts per billion.

Worked number: a vertex costs a factor e, so an amplitude picks up √α ≈ √(1/137.036) ≈ 0.085 per vertex, and every extra loop in a diagram suppresses the result by about α/π ≈ 0.0023. That rapid shrinking is why QED calculations taken to many loops match experiment so well, for example for the electron's magnetic moment.

α is not quite constant. Virtual electron–positron pairs screen charge, so at higher energies the coupling grows: at the Z-boson mass, about 91 GeV, 1/α ≈ 128. Feynman, Schwinger and Tomonaga, who made QED calculations consistent, shared the 1965 Nobel Prize in Physics.

The Vertex Smith: "One electron in, one electron out, one photon at the joint. Give me enough of these and I will build you a rainbow."