(redirected from Nonrenormalizable)
Also found in: Dictionary.


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

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.


(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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Planck scale induced small Majorana masses can be generated through nonrenormalizable dim.5 interaction
The underlying reason is that GR is nonrenormalizable and thus not quantizable in the way conventional Quantum Field Theories are quantized.
On the other hand, since the quantum theory of massless gravitons is nonrenormalizable, a natural question is whether one can build a self-consistent gravity theory if the graviton is massive.
On one hand, effective theories based on GR are nonrenormalizable by power counting, since the coupling constant associated with gravitation has inverse canonical mass dimension.
These gap equations involve integrals that have diverging behavior in the high-energy region (this is an artifact of the nonrenormalizable nature of the NJL model).
It can decay to a pair of SM gauge bosons only through nonrenormalizable dimension-5 operators.
With standard model fields one can induce Majorana neutrino masses through the nonrenormalizable dimension-5 operator