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{{quantum field theory}}
In [[theoretical physics]], specifically [[quantum field theory]], a '''beta function''' or '''Gell-Mann–Low 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 by the '''Gell-Mann–Low equation'''<ref>{{Cite book |last=Tsvelik |first=Alexei M. |url=https://www.google.fr/books/edition/Quantum_Field_Theory_in_Condensed_Matter/78t7iDTth2YC?hl=en&gbpv=1&dq=%22Gell-Mann-Low+equation%22+renormalization&pg=PA61&printsec=frontcover |title=Quantum Field Theory in Condensed Matter Physics |date=2007-01-18 |publisher=Cambridge University Press |isbn=978-0-521-52980-8 |language=en}}</ref> or '''renormalization group equation,''' given by
:: <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''.
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==References==
{{notelist}}
{{Reflist}}
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