In theoretical physics Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain natural phenomena in a mathematical form. Its central core is mathematical physics 1, though other conceptual techniques are also used. The goal is to rationalize, explain and predict physical phenomena. The advancement of science depends in, renormalization group (RG) refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at which physical processes occur. A change in scale is called a "scale transformation" or "conformal transformation." The renormalization group is intimately related to "conformal invariance" or "scale invariance," a symmetry by which the system appears the same at all scales (so-called self-similarity In mathematics, a self-similar object is exactly or approximately similar to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals).
As one varies the scale, it is as if one is changing the magnifying power of a microscope viewing the system. The system will generally make a self-similar copy of itself, with slightly different parameters describing the components of the system. The components, or fundamental variables, may be atoms, fundamental particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be "coupling constants" that measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.
For example, an electron appears to be composed of electrons, anti-electrons and photons as one views it at very short distances. The electron at very short distances has a slightly different electric charge than does the "dressed electron" seen at large distances, and this change, or "running," in the value of the electric charge is determined by the renormalization group equation.
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