Beta function (physics)
In theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, β(g), encodes the dependence of a 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 or renormalization group equation, given by β ( g ) = μ ∂ g ∂ μ = ∂ g ∂ ln ( μ ) , {\displaystyle \beta (g)=\mu {\frac {\partial g}{\partial \mu }}={\frac {\partial g}{\partial \ln(\mu )}}~,} and, because of the underlying renormalization group, it has no explicit dependence on μ, so it only depends on μ implicitly through g.