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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 ?
Hence, the purpose of the current study, as a demonstration of the utility of [C.sub.c], is to renormalize and compare three physically significant energy distributions in statistical physics: the energy probability density functions for systems governed by Boltzmann, Bose-Einstein, and Fermi-Dirac statistics.
With our conceptualization of [C.sub.c] complete, we used it to renormalize and compare three physically significant energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions for energy of subatomic particles.
Here, [[phi].sub.k] denotes the octet of would-be Goldstone bosons ([pi], K, [[eta].sub.8]) arising out of spontaneous breaking of chiral SU[(3).sub.L] [cross product] SU[(3).sub.R] symmetry, [[eta].sub.0] is the singlet boson, and Q is the topological charge density; [chi] = diag[[m.sup.2.sub.[pi]], [m.sup.2.sub.[pi]], (2[m.sup.2.sub.k] - [m.sup.2.sub.[pi]])] is the meson mass matrix, the pion decay constant [F.sub.[pi]] = 92.4 MeV, and [F.sub.0] renormalizes the flavor-singlet decay constant.
In (7), the stability condition truncates and renormalizes f([[theta].sup.T]|Q) to eliminate explosive [theta]'s.
If the parties propose theories [t.sup.1] and [t.sup.2], then any voter s with prior [Phi] revises the probability distribution by assigning probability zero to the event T\[[t.sup.1], [t.sup.2]] and renormalizes the prior on the interval [[t.sup.1], [t.sup.2]].