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 , the antifermion , and the vector potential A.

DefinitionEdit

The vertex function   can be defined in terms of a functional derivative of the effective action Seff as

 
 
The one-loop correction to the vertex function. This is the dominant contribution to the anomalous magnetic moment of the electron.

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 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:

 

NotesEdit

ReferencesEdit

  • Gross, F. (1993). Relativistic Quantum Mechanics and Field Theory (1st ed.). Wiley-VCH. ISBN 978-0471591139.
  • Peskin, Michael E.; Schroeder, Daniel V. (1995). An Introduction to Quantum Field Theory. Reading: Addison-Wesley. ISBN 0-201-50397-2.
  • Weinberg, S. (2002), Foundations, The Quantum Theory of Fields, I, Cambridge University Press, ISBN 0-521-55001-7

External linksEdit