A procedure used in relativistic quantum field theory to deal with the fact that in perturbation theory calculations give rise to infinities beyond the first term. Renormalization was first used in quantum electrodynamics, where the infinities were removed by taking the observed mass and charge of the electron as ‘renormalized’ parameters rather than the ‘bare’ mass and charge.

Theories for which finite results for all perturbation-theory calculations exist, by taking a finite number of parameters from experiment and using renormalization, are called renormalizable. Only certain types of quantum field theories are renormalizable. Theories that need an infinite number of parameters are said to be nonrenormalizable and are regarded as incomplete physical theories. The gauge theories that describe the strong, weak, and electromagnetic interactions are renormalizable. The quantum theory of gravitational interactions is a nonrenormalizable theory, which perhaps indicates that gravity needs to be unified with other fundamental interactions before one can have a consistent quantum theory of gravity. Renormalization theory has been expressed in terms of noncommutative geometry.