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 (Shifman–Vainshtein–Zakharov 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.
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