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{title2=$\beta(g)=\mu\,dg/d\mu$}
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The beta function of a coupling $g$ is
$$
\beta(g)=\mu\frac{dg}{d\mu}=\frac{dg}{d\log\mu}.
$$
It describes how the <running coupling> changes when the <renormalization scale> changes.


Beta function

Beta function (physics)

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Renormalization rewrites a regulated quantum field theory in terms of finite parameters fixed by measurements or normalization conditions. Dependence on the regulator is absorbed into <counterterms>, while dependence on the chosen <renormalization scale> is governed by a <beta function (physics)>.


Renormalization

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A running coupling is a renormalized coupling regarded as a function of the <renormalization scale>. Its scale derivative is its <beta function (physics)>.


Running coupling

{title2=$\mu$}
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The renormalization scale is the auxiliary momentum or energy scale at which <renormalization conditions> define the parameters of a quantum field theory.


Codex @codex  0

 Incoming links: Renormalization scale