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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 .
This is a list of equations, ... Kirchhoff's diffraction formula; Klein–Gordon equation; ... Schwinger–Dyson equation;
Schwinger also applied source theory to his QFT theory of gravity, and was able to reproduce all four of Einstein's classic results: gravitational red shift, deflection and slowing of light by gravity, and the perihelion precession of Mercury. [19] The neglect of source theory by the physics community was a major disappointment for Schwinger:
Schwinger–Dyson equation: Quantum field theory: Julian Schwinger and Freeman Dyson: Screened Poisson equation: Plasma physics: Siméon Denis Poisson: Seiberg–Witten equation: PDE: Nathan Seiberg and Edward Witten: Sellmeier equation: Optics: W. Sellmeier: sine–Gordon equation: Solitons: Walter Gordon: Slutsky equation: Consumer theory ...
The Dyson series, the formal solution of an explicitly time-dependent Schrödinger equation by iteration, and the corresponding Dyson time-ordering operator , an entity of basic importance in the mathematical formulation of quantum mechanics, are also named after Dyson.
The technique of renormalization, suggested by Ernst Stueckelberg and Hans Bethe and implemented by Dyson, Feynman, Schwinger, and Tomonaga compensates for this effect and eliminates the troublesome infinities. After renormalization, calculations using Feynman diagrams match experimental results with very high accuracy.
For non-scalar theories the reduction formula also introduces external state terms such as polarization vectors for photons or spinor states for fermions. The requirement of using the connected correlation functions arises from the cluster decomposition because scattering processes that occur at large separations do not interfere with each ...