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The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between correlation functions in quantum field theories (QFTs).
In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams .
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In 1941, Rarita and Schwinger focussed on spin-3 ⁄ 2 particles and derived the Rarita–Schwinger equation, including a Lagrangian to generate it, and later generalized the equations analogous to spin n + 1 ⁄ 2 for integer n. In 1945, Pauli suggested Majorana's 1932 paper to Bhabha, who returned to the general ideas introduced by Majorana ...
Dyson coined the term "green technologies", based on biology instead of physics or chemistry, to describe new species of microorganisms and plants designed to meet human needs. He argued that such technologies would be based on solar power rather than the fossil fuels whose use he saw as part of what he calls "gray technologies" of industry.
Dirac equation, the relativistic wave equation for electrons and positrons; Gardner equation; Klein–Gordon equation; Knizhnik–Zamolodchikov equations in quantum field theory; Nonlinear Schrödinger equation in quantum mechanics; Schrödinger's equation [2] Schwinger–Dyson equation; Yang-Mills equations in gauge theory
From the mathematical point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization . Since it is equivalent to the differential time-independent Schrödinger equation with appropriate boundary conditions, it can also be solved by numerical methods for ...
Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. Using the well-known observation that 1 A n = 1 ( n − 1 ) ! ∫ 0 ∞ d u u n − 1 e − u A , {\displaystyle {\frac {1}{A^{n}}}={\frac {1}{(n-1)!}}\int _{0}^{\infty }du\,u^{n-1}e^{-uA},}