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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


(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 ?
"Favourable perceptions of regular smoking among this age group also fell at a faster rate after the proliferation of e-cigarettes, which would not be expected if smoking was in the process of being 'renormalised'," the authors concluded.
Starting from a renormalised action on scale [[LAMBDA].sub.0], the flow is going to generate the renormalised action on all lower scaled [LAMBDA], which is the second momentum scale involved.
It should be noted that the renormalised action S[[LAMBDA]], also called Wilsonian effective action, is not identical to the field theoretic effective action [GAMMA], which generates the one-particle irreducible vertex functions.
which, expressed in renormalised fields, is exactly of the same form as (96).
One can now see that due to the effect of the rescaling of the cutoff function, the renormalised kinetic action indeed does not scale.
Since the axial current is not conserved, [G.sub.A] is renormalised by the strong interactions and possibly by non-Standard Model contributions to the weak interactions [2].
The Wickens-Breusch solution to this problem is to reparameterise equation A so that the levels term in C is taken to the left-hand side, and the equation is renormalised using the coefficient estimate obtained in equation A.