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 , the antifermion , and the vector potential A. But the use of a vertex function is not limited to QED.
Definition The vertex function can be defined in terms of a functional derivative of the effective action Seff as
The dominant (and classical) contribution to 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:
where , 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 factors, 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
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