Renormalizable

Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions.

For example, a theory of the electron may begin by postulating a mass and charge. However, in quantum field theory this electron is surrounded by a cloud of possibilities of other virtual particles such as photons, which interact with the original electron. Taking these interactions into account shows that the electron-system in fact behaves as if it had a different mass and charge. Renormalization replaces the originally postulated mass and charge with new numbers such that the observed mass and charge matches those originally postulated.

Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill-defined. To define them, this continuum limit—the removal of the "construction scaffolding" of lattices at various scales—has to be taken carefully. Renormalization procedures are based on the requirement that certain physical quantities are equal to the observed values.

Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics.

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