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 ?
Also, any effort to renormalize policy would include signaling a clear intention to remove the commitment to maintain the federal funds rate at 0 to 1/4 percent "for an extended period.
That is, decision makers consistently overvalue that which they come to possess, suggesting that individuals (and states) will renormalize for gains more quickly than they will renormalize for losses (Levy 1992, 290).
Now we renormalize the fermions propagator to give the real states and let a [right arrow] 0.
When grades are ordinal with unknown cutoffs and unknown noise, however, it is possible to renormalize the structure.
k] matrix and has no effect unless we renormalize the columns of A, after computing the decomposition, we rescale each column of ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) so that it has Euclidean norm one.
We do not renormalize the PAA concentration, m, due to shrinkage in Eq 3a, which in turn would effectively enhance the generation rate in Eq 5.
The images are 9 9 grayscale and we renormalize them to 20 x 20.
Nevertheless, this did not put end to the original problem, which gave rise to greater problems and reproach, scattered between attempts to find bilateral and regional approaches to renormalize relations, attempts which ended by the consecration of the state of paralysis.
With no loss in generality, we can normalize c(q) = q, as long as we also renormalize u(q).
The goal is to complete them in a way that retrains and renormalizes visual processing to improve visual attention, state of processing and working memory," said Hardy.
2] is the adjusted generalized coefficient of determination proposed by Nagelkerke (1991), which renormalizes Cox and Shell's (1989) [R.
To measure whether airlines, airports, or the TSA became more efficient in handling airport closures over time, we create the variable "event date," which renormalizes the airport closure date between 0 (September 11, 2001) and 1 (September 11, 2002).