Sum rules

Sum rules

Formulas in quantum mechanics for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form. Sum rules are used to describe the properties of many physical systems, including solids, atoms, atomic nuclei, and nuclear constituents such as protons and neutrons. The sum rules are derived from quite general principles, and are useful in situations where the behavior of individual energy levels is too complex to describe by a precise quantum-mechanical theory. See Energy level (quantum mechanics)

In general, sum rules are derived by using Heisenberg's quantum-mechanical algebra to construct operator equalities, which are then applied to particles or the energy levels of a system. See Quantum mechanics

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
They lead to the following QCD sum rules where we have computed the operator product expansion up to the eighth dimension:
Many neutrino mass models predict relations such as neutrino mass sum rules [41, 100-106] that can be probed in neutrinoless double beta decay [107] and relations among the neutrino mixing parameters.
Quantitative information regarding the orbital ([[mu].sub.L]) and spin ([[mu].sub.S]) components to the total magnetic moment per Co ion ([[mu].sub.TOT]) was calculated by applying sum rules [21, 23], where we have explicitly included the magnetic dipole term ([[mu].sub.T]) for the as-deposited and annealed films.
The volume also reproduces three of his articles on new exact heavy quark sum rules, QCD predictions for lepton spectra in inclusive heavy flavor decays, and high power n of mb in b-flavored widths and n equals five to the limit of infinity.
With the two-scale similarity transform (TST) in the hand, we further discuss the properties of polynomial reproduction with respect to the general subdivision symbol satisfying certain order of sum rules. For TST, see [6,13,15,16] and references therein.
Among the topics are the validity of random matrix theories for many-particle systems, the angular-momentum dependence of the density of states, group theory and the propagation of operator averages, electromagnetic sum rules by spectral distribution methods, compound-nuclear tests of time reversal invariance in the nucleon-nucleon interaction, strength functions and spreading widths of simple shell model configurations, and underlying symmetries of realistic interactions and the nuclear many-body problem.
We say that a satisfies the sum rules of order s if a has a zero of order s at [gamma], for all [gamma] [member of] [GAMMA]\{0}.
A few examples of specific topics include the latest experimental results on pentaquarks, an overview of spin physics, deconstructed Higgsless models, approximated Faddeev-Niemi knotted solitons, topological susceptibility in the SU(3) gauge theory, finite temperature lattice gauge theories in external fields, sum rules for leading and subleading form factors in heavy quark effective theory using the non-forward amplitude, and quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces.
(11) An estimate of k [30] using factorization and QCD sum rules yielded k [equivalent] 10, implying
In this study, 3-point sum rules (3PSR) method is used to calculate the strong form factors and coupling constants of the [D.sup.*.sub.s][D.sup.*] [K.sup.*] and [D.sub.s1][D.sub.1][K.sup.*] vertices.
We say that [??]([xi]) has m sum rules if there exists a 1 x r matrix [??]([xi]): = ([[??].sub.1]([xi]), [[??].sub.2]([xi]), ..., [[??].sub.r]([xi])) of 2[pi]-periodic trigonometric polynomials with [??](0) [not equal to] 0 such that