Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.

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, as detailed below. Renormalization procedures are based on the requirement that certain physical quantities are equal to the observed values.