Sum rule
Encyclopedia
Sum rule may refer to:
- Sum rule in differentiationSum rule in differentiationIn calculus, the sum rule in differentiation is a method of finding the derivative of a function that is the sum of two other functions for which derivatives exist. This is a part of the linearity of differentiation. The sum rule in integration follows from it...
- Sum rule in integrationSum rule in integrationIn calculus, the sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. It is of particular use for the integration of sums, and is one part of the linearity of integration....
- Rule of sumRule of sumIn combinatorics, the rule of sum or addition principle is a basic counting principle. Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing and we can not do both at the same time, then there are a + b ways to choose one of the...
, a counting principle in combinatorics - Sum rule in quantum mechanicsSum rule in quantum mechanicsIn quantum mechanics, a sum rule is a formula for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form...
- in quantum field theoryQuantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, 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 currentsCurrent algebraCurrent algebra is a mathematical framework in quantum field theory where the fields form a Lie algebra under their commutation relations.For instance, in a non-Abelian Yang–Mills symmetry, where ρ is the charge density,...
, the Adler Weissberger sum rule gives the normalization of weak interaction strength in terms of pion scattering amplitudes, the SVZ sum rules (ShifmanMikhail Shifman-External links:*****...
–Vainshtein–Zakharov sum rules) in quantum chromodynamicsQuantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
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 theoryString theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
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