Editing Quantum electrodynamics (section)

==Renormalizability==
Higher-order terms can be straightforwardly computed for the evolution operator, but these terms display diagrams containing the following simpler ones<ref name=Peskin/>{{rp|ch 10}}

<gallery class="center">
Image:vacuum_polarization.svg | One-loop contribution to the [[vacuum polarization]] function <math>\Pi</math>
Image:electron_self_energy.svg | One-loop contribution to the electron [[self-energy]] function <math>\Sigma</math>
Image:vertex_correction.svg | One-loop contribution to the [[vertex function]] <math>\Gamma</math>
</gallery>

that, being closed loops, imply the presence of diverging [[integral]]s having no mathematical meaning. To overcome this difficulty, a technique called [[renormalization]] has been devised, producing finite results in very close agreement with experiments. A criterion for the theory being meaningful after renormalization is that the number of diverging diagrams is finite. In this case, the theory is said to be "renormalizable". The reason for this is that to get observables renormalized, one needs a finite number of constants to maintain the predictive value of the theory untouched. This is exactly the case of quantum electrodynamics displaying just three diverging diagrams. This procedure gives observables in very close agreement with experiment as seen e.g. for electron [[gyromagnetic ratio]].

Renormalizability has become an essential criterion for a [[quantum field theory]] to be considered as a viable one. All the theories describing [[fundamental interaction]]s, except [[gravitation]], whose quantum counterpart is only conjectural and presently under very active research, are renormalizable theories.