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 ψ {displaystyle psi } , the antifermion ψ ¯ {displaystyle {ar {psi }}} , and the vector potential A. 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 ψ {displaystyle psi } , the antifermion ψ ¯ {displaystyle {ar {psi }}} , and the vector potential A. The vertex function Γ μ {displaystyle Gamma ^{mu }} can be defined in terms of a functional derivative of the effective action Seff as The dominant (and classical) contribution to Γ μ {displaystyle Gamma ^{mu }} is the gamma matrix γ μ {displaystyle gamma ^{mu }} , 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 σ μ ν = ( i / 2 ) [ γ μ , γ ν ] {displaystyle sigma ^{mu u }=(i/2)} , q ν {displaystyle q_{ u }} is the incoming four-momentum of the external photon (on the right-hand side of the figure), and F1(q2) and F2(q2) are form factors that depend only on the momentum transfer q2. At tree level (or leading order), F1(q2) = 1 and F2(q2) = 0. Beyond leading order, the corrections to F1(0) are exactly canceled by the field strength renormalization. The form factor F2(0) corresponds to the anomalous magnetic moment a of the fermion, defined in terms of the Landé g-factor as: