renormalization

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Renormalization

A program in quantum field theory consisting of a set of rules for calculating S-matrix amplitudes which are free of ultraviolet (or short-distance) divergences, order by order in perturbative calculations in an expansion with respect to coupling constants. See Scattering matrix

So far the only field theories known to be renormalizable in four dimensions are those which include spin-0, spin-1/2, and spin-1 fields such that no term in the lagrangian exceeds operator dimension 4. The operator dimension of any term is calculated by assigning dimension 1 to bosons and derivatives ∂μ, and dimension 3/2 to fermions. Spin-1 fields are allowed only if they correspond to the massless gauge potentials of a locally gauge-invariant Yang-Mills-type theory associated with any compact Lie group. The gauge invariance can remain exact or can be allowed to break via spontaneous breakdown without spoiling the renormalizability of the theory. In the latter case the spin-1 field develops a mass. The successful quantum chromodynamics theory describing the strong forces and the SU(2) × U(1) Weinberg-Salam-Glashow gauge model of unified electroweak particle interactions are such renormalizable gauge models containing spin 0, 1/2, and 1 fields. See Electroweak interaction, Fundamental interactions, Quantum chromodynamics, Quantum electrodynamics, Weak nuclear interactions

Effective field theory is a general and powerful method for analyzing quantum field theories over a wide range of length scales. Together with a closely related idea, the Wilson renormalization group, it places renormalization theory on a more general, physical, and rigorous basis. This method is most naturally developed in the Feynman path integral formulation of quantum field theory, where amplitudes are given by an integral over all histories. Each history is weighted by a phase equal to the classical action divided by Planck's constant. See Action

renormalization

[rē‚nȯr·mə·lə′zā·shən]
(quantum mechanics)
In certain quantum field theories, a procedure in which nonphysical bare values of certain quantities such as mass and charge are eliminated and the corresponding physically observable quantities are introduced.
References in periodicals archive ?
The researchers say: "Our results provide little evidence that renormalisation of smoking occurred during this period.
The renormalisation group has been used to derive the semicircle law for random matrices in the pioneering work of Brezin and Zee [4].
where (25a) refers to a convergent generating function, and (25b) to a generating function which is divergent at r = 0 and where a special renormalisation procedure has to be applied.
Then, starting from the action contained in the functional integral, we formulate a renormalisation group transformation.
Section 2.2 defines convenient renormalisations [h.sup.g.sub.n] ([??]) and [H.sup.g.sub.n] ([??]).
There was significant renormalisation of the biochemical parameters of liver functions after 30 days of treatment with the herbal formulation.
Schindler [1998] describes a further method that allows byte-by-byte output from the renormalisation loop, based upon the loop guard R [is less than] [2.sup.b-9] that delays any action until eight bits are determined.
He also did Ph.D in Theoretical Physics in 1952 on 'renormalisation theory.
Stephenson, "The effective potential and the renormalisation group," Nuclear Physics B, vol.
But the Labour Government said most places on the proscribed list were those where there was the greatest risk of the "renormalisation" of smoking for youngsters, and the amendments put forward by ministers were agreed by seven votes to three by the Assembly's health and social care committee.