Renormalization group

In theoretical physics, the renormalization group (RG) is a mathematical tool that allows systematic investigation into the changes in a physical system as it is viewed at different scales. The scales of the system typically describe the interactions of the objects; they may be variable ("running") couplings which measure the strength of various forces, mass parameters, or the size of the system. The renormalization group is related to scale invariance and conformal invariance, symmetries in which a system exhibits self-similarity; in some cases, the parameters of the model can be assigned to special values, known as a "fixed point", where the field theory is conformally invariant and any running couplings cease to change. In particle physics, this treatment reflects the changes in the underlying physical laws (codified in a quantum field theory that is renormalizable) as the energy or mass scale at which physical processes occur varies. For example, in quantum electrodynamics (QED), an electron appears to be composed of electron and positron pairs and photons at very short distances. Taken together, this set of particles has a slightly different electric charge than the dressed electron seen at large distances, and this change in the value of the charge is determined by the renormalization group equation.