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Please enable it for a better experience of Jumi. For example, a theory of the electron may begin by postulating a mass and charge. However, in quantum field theory this electron is surrounded by a cloud of possibilities of other virtual particles such as photons, which interact with the original electron. Taking these interactions into account shows that the electron-system in fact behaves as if it had a different mass and charge. 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.
Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales. The problem of infinities first arose in the classical electrodynamics of point particles in the 19th and early 20th century. This implies that the point particle would have infinite inertia, making it unable to be accelerated. If the shell’s bare mass is allowed to be negative, it might be possible to take a consistent point limit. When calculating the electromagnetic interactions of charged particles, it is tempting to ignore the back-reaction of a particle’s own field on itself. Analogous to the back-EMF of circuit analysis. 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. This loop has a logarithmic ultraviolet divergence. Such a particle is called off-shell. When there is a loop, the momentum of the particles involved in the loop is not uniquely determined by the energies and momenta of incoming and outgoing particles.
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