Renormalization

Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. Even if no infinities arose in loop diagrams in quantum field theory, it can be shown that it is necessary to renormalize the mass and fields appearing in the original Lagrangian. This is the dominant method used in theoretical physics to treat these divergent quantities due its broad applicability, though more limited but rigorous approaches like causal perturbation theory are also used. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in this example, mathematically replaces the initially postulated mass and charge of an electron (the bare particle) with the experimentally observed mass and charge (the dressed particle). Mathematics and experiments prove that positrons and more massive particles such as protons exhibit precisely the same observed charge as the electron – even in the presence of much stronger interactions and more intense clouds of virtual particles. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. Renormalization specifies relationships between parameters in the theory when parameters describing large distance scales differ from parameters describing small distance scales. Physically, the pileup of contributions from an infinite number of scales involved in a problem...