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 ?
3, evaluations were done using mass attenuation and mass energy-transfer coefficients based on both unrenormalized and renormalized photoelectric-absorption cross sections.
Notice that the quantity [absolute value of [mu]] - l([mu]) is not changed if one adds or removes parts of size 1 to the integer partition In the following, we shall rather work with renormalized character values [[summation].
The top 25 phrases are chosen as the key phrases for the target Web site and their weights are renormalized.
Of course, the summed probabilities--even if renormalized to lie in the unit interval cannot be interpreted formally as a probability because the regime-switching process was specified individually for each index, not jointly across all indexes.
Both the Spanish WISC-R for child IQ and the Spanish Wechsler Adult Intelligence Scale used for maternal IQ have since been superseded by updated, renormalized versions.
The prices used were ones that were as close to original purchase prices as possible, renormalized to base years of 1977 and 1987 with the Producer Price Index (PPI) for aircraft and the PPI for engines.
It is consistent because the equation can be renormalized to include the difference between the final GDP estimate and the long-run average of GDP; only the constant term is affected.
Instead of using cut-off masses and renormalized charges, proper normalization includes a proper normalization factor for each propagator.
Motivated by these expectations, the measure of teachers' grading is renormalized such that a larger number implies harder grading.
The distribution of completed spells for those eligible to receive the EITC at a point in time is the distribution of new spells weighted by duration and renormalized.
So, the relative crystallinity curves were renormalized in such a way that they became equal to unity for the temperature corresponding to this intersection.
Quite simply, all membership function values less than a are replaced with zero and the function is renormalized (sums to one) to preserve partition condition (1).