In quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory

Perturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

. In particular, it is the one particle irreducible correlation function involving the fermion

Fermion

In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

 , the antifermion , and the vector potential

Vector potential

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field....

 A.

Definition

The vertex function Γ^μ can be defined in terms of a functional derivative

Functional derivative

In mathematics and theoretical physics, the functional derivative is a generalization of the gradient. While the latter differentiates with respect to a vector with discrete components, the former differentiates with respect to a continuous function. Both of these can be viewed as extensions of...

 of the effective action

Effective action

In quantum field theory, the effective action is a modified expression for the action, which takes into account quantum-mechanical corrections, in the following sense:...

 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

Polarization

Polarization is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves in a gas or liquid do not have polarization because the direction of vibration and...

of the photon, as expressed by the Ward identity; and invariance under parity

Parity (physics)

In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

 -- to take the following form:


where , 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 wave function renormalization

Wave function renormalization

In quantum field theory, wave function renormalization is a rescaling, or renormalization, of quantum fields to take into account the effects of interactions. For a noninteracting or free field, the field operator creates or annihilates a single particle with probability 1. Once interactions are...

 of the incoming and outgoing electron lines according to the Ward-Takahashi identity. The form factor F₂(0) corresponds to the anomalous magnetic moment a of the fermion, defined in terms of the Lande g-factor

Landé g-factor

In physics, the Landé g-factor is a particular example of a g-factor, namely for an electron with both spin and orbital angular momenta. It is named after Alfred Landé, who first described it in 1921....

as: