In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion, and the vector potential A. But the use of a vertex function is not limited to QED.

Definition

can be defined in terms of a functional derivative of the effective action Seff as

is the gamma matrix, which explains the choice of the letter. The vertex function is constrained by the symmetries of quantum electrodynamics — Lorentz invariance; gauge invariance or the transversality of the photon, as expressed by the Ward identity; and invariance under parity — to take the following form:

is the incoming four-momentum of the external photon (on the right-hand side of the figure), and and are the Dirac and Pauli form factorss, respectively, that depend only on the momentum transfer q2. At tree level (or leading order), and . Beyond leading order, the corrections to are exactly canceled by the field strength renormalization. The form factor corresponds to the anomalous magnetic moment a of the fermion, defined in terms of the Landé g-factor as:

In 1948, Julian Schwinger calculated the first correction to anomalous magnetic moment, given by where α is the fine-structure constant.

See also

• Nonoblique correction

References

External links