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In 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. 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.
In quantum field theory, a sum rule is a relation between a static quantity and an integral over a dynamical quantity. Therefore, they have a form such as: =where () is the dynamical quantity, for example a structure function characterizing a particle, and is the static quantity, for example the mass or the charge of that particle.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
The QCD sum rules (or Shifman–Vainshtein–Zakharov sum rules) are a way of dealing with this. The idea is to work with gauge invariant operators and operator product expansions of them. The vacuum to vacuum correlation function for the product of two such operators can be reexpressed as
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.