Editing Beta function (physics) (section)

{{Short description|Function that encodes the dependence of a coupling parameter on the energy scale}}
{{About|the beta functions of theoretical physics|other beta functions|Beta function (disambiguation)}}

{{quantum field theory}}

In [[theoretical physics]], specifically [[quantum field theory]], a '''beta function''', ''β(g)'', encodes the dependence of a [[Coupling constant|coupling parameter]], ''g'', on the [[energy scale]],  ''μ'',  of a given physical process described by [[quantum field theory]].
It is defined as
:: <math>\beta(g) = \mu \frac{\partial g}{\partial \mu} = \frac{\partial g}{\partial \ln(\mu)} ~,</math>
and, because of the underlying  [[renormalization group]], it has no explicit dependence on ''μ'', so it only depends on ''μ'' implicitly through  ''g''.
This dependence on the energy scale thus specified is known as the [[Coupling constant#Running coupling|running]] of the coupling parameter, a fundamental 
feature of  scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques. The concept of Beta function was Introduced by [[Ernst Stueckelberg]] and [[André Petermann]] in 1953.<ref>{{cite journal |author1-link=Ernst Stueckelberg |last1=Stueckelberg |first1=E.C.G. |author2-link=André Petermann |first2=A. |last2=Petermann |year=1953 |url=https://www.e-periodica.ch/cntmng?pid=hpa-001:1953:26::894 |title=La renormalisation des constants dans la théorie de quanta |journal=Helv. Phys. Acta |volume=26 |pages=499–520 |language=FR}}</ref>