Sum rule

From Wikipedia, the free encyclopedia

Sum rule may refer to:

• Sum rule in differentiation
• Sum rule in integration
• Rule of sum, a counting principle in combinatorics
• In quantum mechanics, sum rule refers to formulas 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. 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 also selection rule.
• in quantum field theory, a sum rule is a property of the sum of the scattering probability over all energies which is independent of the particular dynamical details and can be calculated precisely. It is a special case of a quantum mechanical sum rule, with specific applications. In the theory of quark currents, the Adler Weissberger sum rule gives the normalization of weak interaction strength in terms of pion scattering amplitudes, the SVZ sum rules in quantum chromodynamics predict some of the low-lying meson properties from some universal vacuum parameters and short distance quark-gluon interactions, while the finite energy sum rules are phenomenological properties of the hadronic spectral density which were significant for the discovery of string theory.