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 ?
However, they are renormalizable below decoupling temperatures.
This property of renormalizable is as a property related to the gauge invariance.
The starting point is always the SM Lagrangian, complemented with a DM particle and a mediator that couples to it, through renormalizable operators, to quarks and gluons, which is necessary for the production of these states at a hadron collider.
If one sets aside the algebraic convergence problems when working with Clifford algebras in infinite dimensions, one can consider the possibility of studying Quantum Gravity in a very large number of dimensions which has been revisited recently [83] in connection to a perturbative renormalizable quantum theory of gravity in infinite dimensions.
Maskawa, "CP violation in the renormalizable theory of weak interaction," Progress of Theoretical and Experimental Physics, vol.
Higher-derivative gravity is the only model that is known to be renormalizable along its matter couplings up to now [30].
Since, in contrast to the other fermions, right-handed partners of the SM left-handed neutrinos are missing in the SM particle content, the SM neutrinos cannot acquire their masses at the renormalizable level, even after the electroweak symmetry is broken.
Kobayashi and T Maskawa, "CP-violation in the renormalizable theory of weak interaction," Progress of Theoretical and Experimental Physics, vol.
In this section, we would briefly review the UV complete theory of gravity which is a nonrelativistic renormalizable theory of gravity known as Horava Lifshitz [23-25] gravity.
The R-parity violating gauge invariant and renormalizable superpotential is [42, 48, 49]
In a renormalizable theory, the change in orbital angular momentum is limited to [DELTA][L.sup.z] = 0, [+ or -] 1 at each vertex [52].