Renormalization

In quantum field theory (QFT) and the statistical mechanics of fields, renormalization refers to a collection of techniques used to express physical calculations in terms of observable quantities that already include some field effects. Renormalization arose in quantum electrodynamics as a means of making sense of the infinite results of various calculations and extracting finite answers to properly posed physical questions. Initially viewed as a suspect, provisional procedure by most of its originators, renormalization eventually was embraced as an important tool in several fields of physics, as a result of work in effective field theory and the renormalization group.

Prehistory: Self-interactions in classical mechanics

Some of the problems and phenomena eventually addressed by renormalization actually appeared earlier in the classical electrodynamics of point particles in the 19th and early 20th century. When calculating the electromagnetic interactions of charged particles, one often ignores the back-reaction of a particle's own field upon itself. It was realized early on that such a treatment is incomplete, and some theorists explored the intriguing idea that an electron's inertial mass could be entirely due to the back-reaction. However, if the electron is assumed to be a point, the calculated value of this back-reaction diverges, essentially because of the singularity at the origin in the inverse-square law. One potential solution was to assume that, say, the electron had a nonzero size, comparable to the number known as the classical electron radius, about 2.8 x 10-15m. Then, however, according to Henri Poincaré, the theory became inconsistent unless the electron possessed additional forces to hold it together internally against the repulsion of like charges. Today the hypothesis of a classical electron radius might be seen as an early attempt at regularization. Attempts to deal with the back-reaction, such as the Abraham-Lorentz theory, were never entirely internally consistent and exhibited bizarre phenomena such as anti-causal "pre-acceleration", in which an electron would start moving shortly before a force was applied (Jackson 1998).

Related Topics:
Classical electrodynamics - Particle - 19th - 20th century - Electromagnetic - Charged - Electron - Inertial - Mass - Inverse-square law - Classical electron radius - Henri Poincaré - Regularization - Abraham-Lorentz theory

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In classical field theory, therefore, the contribution of field interactions to a particle's physical properties was already problematic. Indeed, in some ways the trouble was worse than in QFT, since the short-distance divergences involved were typically stronger than the ones encountered in quantum theories.

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