Beta Function

The beta function (or β-function) in quantum field theory encodes how the coupling constants of an interaction change as the energy scale changes. It is the generator of the renormalization group flow in the space of couplings: the differential equation dg/dln(μ) = β(g) determines whether a coupling grows, shrinks, or remains constant as the observation scale μ changes. The zeros of the beta function are the fixed points of the renormalization group — points where the theory becomes scale-invariant and the concept of running