Editing Beta function (physics) (section)

===Quantum electrodynamics===
{{Main|Quantum electrodynamics}}
The one-loop beta function in [[quantum electrodynamics]] (QED) is

*<math>\beta(e)=\frac{e^3}{12\pi^2}~,</math>
or, equivalently,
*<math>\beta(\alpha)=\frac{2\alpha^2}{3\pi}~,</math>

written in terms of the [[Fine-structure constant#In non-SI units|fine structure constant]] in natural units, {{math|''α'' {{=}}  ''e''<sup>2</sup>/4π}}.<ref>{{cite book |last1=Srednicki |first1=Mark Allen |title=Quantum field theory |date=2017 |publisher=Cambridge Univ. Press |location=Cambridge |isbn=978-0-521-86449-7 |page=446 |edition=13th printing}}</ref>

This beta function tells us that the coupling increases with increasing energy scale, and QED becomes strongly coupled at high energy. In fact, the coupling apparently becomes infinite at some finite energy, resulting in a [[Landau pole]]. However, one cannot expect the perturbative beta function to give accurate results at strong coupling, and so it is likely that the Landau pole is an artifact of applying perturbation theory in a situation where it is no longer valid.