Vertex function

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 ${\displaystyle \psi }$, the antifermion ${\displaystyle {\bar {\psi }}}$, and the vector potential A.

The vertex function Γ^μ can be defined in terms of a functional derivative of the effective action S_eff as

The dominant (and classical) contribution to Γ^μ is the gamma matrix γ^μ, 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:

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