the domain of divergent momentum integrals to be below some momentum cut-off , obtain expressions for the physical quantities, and then take the limit . This is an example of regularization, a class of methods to treat divergences in QFT, with being the regulator. The approach illustrated above is called bare perturbation theory, as calculations involve only the bare quantities such as mass and coupling constant. A different approach, called renormalized perturbation theory, is to use physically meaningful quantities from the very beginning. In the case of theory, the field strength is first redefined: where is the bare field, is the renormalized field, and is a constant to be determined. The Lagrangian density becomes: where and are the experimentally measurable, renormalized, mass and coupling constant, respectively, and are constants to be determined. The first three terms are the Lagrangian density written in terms of the renormalized quantities, while the latter three terms are referred to as "counterterms". As the Lagrangian now contains more terms, so the Feynman diagrams should include additional elements, each with their own Feynman rules. The procedure is outlined as follows. First select a regularization scheme (such as the cut-off regularization introduced above or dimensional regularization); call the regulator . Compute Feynman diagrams, in which divergent terms will depend on . Then, define , , and such that Feynman diagrams for the counterterms will exactly cancel the divergent terms in the normal Feynman diagrams when the limit is taken. In this way, meaningful finite quantities are obtained. It is only possible to eliminate all infinities to obtain a finite result in renormalizable theories, whereas in non-renormalizable theories infinities cannot be removed by the redefinition of a small number of parameters. The Standard Model of elementary particles is a renormalizable QFT, while quantum gravity is non-renormalizable. Renormalization group The renormalization group, developed by Kenneth Wilson, is a mathematical apparatus used to study the changes in physical parameters (coefficients in the Lagrangian) as the system is viewed at different scales. The way in which each parameter changes with scale is described by its β function. Correlation functions, which underlie quantitative physical predictions, change with scale according to the Callan–Symanzik equation. As an example, the coupling constant in QED, namely the elementary charge , has the following β function: where is the energy scale under which the measurement of is performed. This differential equation implies that the observed elementary charge