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 \psi , the antifermion \bar{\psi} , and the vector potential A. But the use of a vertex function is not limited to QED.

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 \psi , the antifermion \bar{\psi} , and the vector potential A. But the use of a vertex function is not limited to QED. ==Definition== The vertex function \Gamma^\mu can be defined in terms of a functional derivative of the effective action S eff as \Gamma^\mu = -{1\over e}{\delta^3 S_{\mathrm{eff}}\over \delta \bar{\psi} \delta \psi \delta A_\mu} The dominant (and classical) contribution to \Gamma^\mu is the gamma matrix \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: \Gamma^\mu = \gamma^\mu F_1(q^2) + \frac{i \sigma^{\mu\nu} q_{\nu}}{2 m} F_2(q^2) where \sigma^{\mu\nu} = (i/2) [\gamma^{\mu}, \gamma^{\nu}] , q_{\nu} 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 q 2 . 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: a = \frac{g-2}{2} = F_2(0) In 1948, Julian Schwinger calculated the first correction to anomalous magnetic moment, given by F_2(0)\approx \frac{\alpha}{2\pi} where α is the fine-structure constant. ==See also== Nonoblique correction ==References== ==External links==

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