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 ?
8 cm) FACs, with a result (using renormalized photoelectricabsorption cross sections) for L = 19 cm estimated to be 1.
They include a duality for the double fibration transform, K-theories for classes of infinite rank bundles, a C*-algebra approach to the index theory of boundary value problems, renormalized integrals and a path integral formula for the heat kernel on the manifold, and ill-posedness examples for the quasi-geostrophic and the Euler equations.
The renormalized entropy, as a measure of relative degree of order, is a further suitable method for the detection of patients at risk for SCD.
2) RDIH: the peak-value and renormalized histogram of difference images;
Whenever subsamples were created, these weights were renormalized within subsamples.
should be renormalized and tempered in its entirety, or as an alternative, the heated portion could be removed from the component for re-normalizing and tempering and then replaced into the component.
If the payoffs to buyers and sellers were to be renormalized by dividing by the standard deviation of the common shock--an innocuous transformation given risk neutrality--those payoffs would be as follows:
The variances of the feature components will also be renormalized according to
Thus, for Schur-Weyl measures, the calculations of linear functionals of the fluctuations involve hypergeometric identities; whereas for Gelfand measures, the problem resides mainly in the proof of the joint convergence of the renormalized character values, and one has to go beyond the setting of asymptotic factorization described in [S06], see Lemma 4.
That success largely reflects the effective design of those programs, as most were structured to provide credit under terms that would be less and less appealing as markets renormalized.
Thus the person components were renormalized, as this typically has the effect of allowing person component scores to be correlated among themselves.