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

References in periodicals archive ?
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.
In case of PRODUCT, MIN, and SUM rules, we do not use any weight for calculating the distance.
Although the MRR of the proposed method based on PRODUCT rule is the same as that based on the sum rule, the Top 1 accuracy of the proposed method is a little higher than that of the sum rule.
The couplings entering into the effective theory can be computed by using non perturbative techniques, and in particular we are interested in the so-called QCD sum rules techniques for heavy flavour physics.
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}.
Therefore, we are interested in the construction of refinable functions with high sum rule order.
In summary, one seeks to construct interpolatory symbols a with high sum rule order and small mask size.
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
For the SUM rules, if the sum of the quality scores of the enrolled and input finger-vein images was greater than the threshold, an attempt was made to match the input image with the enrolled image.
12 (b) show the results with the SUM rules and the AND rules, respectively.