|
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities. Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the "construction scaffolding" of lattices at various scales, has to be taken carefully, as detailed below. Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through "effective" descriptions. ''All scales'' are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each. == Self-interactions in classical physics == The problem of infinities first arose in the classical electrodynamics of point particles in the 19th and early 20th century. The mass of a charged particle should include the mass-energy in its electrostatic field (Electromagnetic mass). Assume that the particle is a charged spherical shell of radius . The mass-energy in the field is : which becomes infinite as . This implies that the point particle would have infinite inertia, making it unable to be accelerated. Incidentally, the value of that makes where is the fine structure constant, and is the Compton wavelength of the electron. The total effective mass of a spherical charged particle includes the actual bare mass of the spherical shell (in addition to the aforementioned mass associated with its electric field). If the shell's bare mass is allowed to be negative, it might be possible to take a consistent point limit. This was called ''renormalization'', and Lorentz and Abraham attempted to develop a classical theory of the electron this way. This early work was the inspiration for later attempts at regularization and renormalization in quantum field theory. When calculating the electromagnetic interactions of charged particles, it is tempting to ignore the ''back-reaction'' of a particle's own field on itself. But this back reaction is necessary to explain the friction on charged particles when they emit radiation. If the electron is assumed to be a point, the value of the back-reaction diverges, for the same reason that the mass diverges, because the field is inverse-square. The Abraham–Lorentz theory had a noncausal "pre-acceleration". Sometimes an electron would start moving ''before'' the force is applied. This is a sign that the point limit is inconsistent. The trouble was worse in classical field theory than in quantum field theory, because in quantum field theory a charged particle experiences Zitterbewegung due to interference with virtual particle-antiparticle pairs, thus effectively smearing out the charge over a region comparable to the Compton wavelength. In quantum electrodynamics at small coupling the electromagnetic mass only diverges as the logarithm of the radius of the particle. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「renormalization」の詳細全文を読む スポンサード リンク
|