Regularization (physics)

In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and has proven to yield useful, accurate predictions. Regularization procedures deal with infinite, divergent, and nonsensical expressions by introducing an auxiliary concept of a regulator (for example, the minimal distance in space which is useful, in case the divergences arise from short-distance physical effects). The correct physical result is obtained in the limit in which the regulator goes away (in our example, ), but the virtue of the regulator is that for its finite value, the result is finite. However, the result usually includes terms proportional to expressions like which are not well-defined in the limit . Regularization is the first step towards obtaining a completely finite and meaningful result; in quantum field theory it must be usually followed by a related, but independent technique called renormalization. Renormalization is based on the requirement that some physical quantities — expressed by seemingly divergent expressions such as — are equal to the observed values. Such a constraint allows one to calculate a finite value for many other quantities that looked divergent.