Renormalization

Procedures of renormalization are used in ɛ quantum field theory to deal with divergent integrals appearing in perturbative calculations of order higher than the lowest one. These ill-defined expressions would seem to render perturbative computations meaningless, thus depriving quantum field theory of an essential tool for obtaining phenomenological predictions. However, in some theories it is possible to circumvent this problem and formally compensate for the divergencies, obtaining for observable quantitites finite predictions which closely match experimental data. This was shown to be possible for ɛ QED in the late 1940s, when the development of renormalization procedures resulted in agreement between theoretical estimates and experimental measurements of the fine and hyperfine structure of the hydrogen spectrum (ɛ spectroscopy; Bohr's atom model).

The central idea of renormalization is to systematically isolate and remove the divergencies by means of a redefinition (renormalization) of the nonperturbed field equation and of its parameters, usually referred to as “bare” masses and charges. Bare parameters are not observable and can therefore be assumed to have exactly those values — finite or infinite — which are needed to compensate for the divergencies. If all infinities can be eliminated by imposing only a finite number of renormalization conditions based on experimental data, the theory is said to be renormalizable. Renormalizability is a nontrivial feature of a theory, because it implies that the potentially infinite number of divergencies occurring in its perturbative expansion can be eliminated at all orders by iterating the same subtraction scheme. Beside QED, other renormalizable theories are ɛ QCD and the Standard Model quantum field theory; particle physics for electro-weak interactions.