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.

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References in periodicals archive

The quantity case-based entropy [5], [C.sub.c], renormalizes the diversity contribution of any probability distribution P(x), by computing the true diversity D of an equiprobable distribution (called the Shannon-equivalent uniform distribution) that has the same Shannon entropy H as P(x).

Advancing Shannon Entropy for Measuring Diversity in Systems

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." As the public adjusts to this, we should then turn to determining the pace at which we return the funds rate to 1 percent.

The Federal Reserve's mandate: long run

Then it is certainly the case that none of the cells (situations) labeled with sneeze = false apply at present; so, in determining the posterior probability that cold = true given sneeze = true, we only sum cells labeled with cold = true and sneeze = true and renormalize (divide by the sum of all cells labeled with sneeze = true regardless of their cold label).

Inference in Bayesian Networks

The scalar [Alpha] controls the splitting of the [[Sigma].sub.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.

A Semidiscrete Matrix Decomposition for Latent Semantic Indexing in Information Retrieval

Even when environments or handicaps create stress for children, relationships with others can protect them from severe damage; children can use a supportive environment to renormalize their development.(16)

The challenge of diversity

RAMALLAH, July 4 (KUNA) -- Turkish humanitarian supplies have arrived in Gaza Strip on Monday after the ship carrying them docked at Israel's Ashdod port yesterday, the first shipment after Ankara and Tel Aviv agreed to renormalize ties.

First Turkish aid arrive in Gaza

We use this modification in calculating the quarks self-energy for the perturbation interaction with the gluons, then we renormalize the interaction and search for the condition [a.sup.2][p.sup.2] [right arrow] 0 and [a.sup.2][k.sup.2] [right arrow] 0.

The dual behavior of quantum fields and the Big Bang

And at the height of the escalation of the desert war, Morocco and Algeria vowed to renormalize their bilateral relations.

The Borders of Morocco and Algeria

Regardless of how the chiral expansion is organized, the issue of how to renormalize the two-body interaction is of fundamental importance and has been subject of investigation for decades.

Renormalization of Chiral Nuclear Forces with Multiple Subtractions in Peripheral Channels

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.

The Concerns of the Border between Morocco and Algeria

Innovate's lead drug candidate, larazotide acetate, has a mechanism of action that renormalizes the dysfunctional intestinal barrier by decreasing intestinal permeability and reducing antigen trafficking, such as gliadin fragments in celiac disease, and bacterial toxins and immunogenic antigens in NASH.

Innovate Biopharmaceuticals Inc. Announces First Patient Dosed in the First Phase 3 Clinical Trial for Patients with Celiac Disease