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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).
The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this algorithm grows asymptotically as 3 n, where n is the number of particles involved in the process, compared to n! in the traditional Feynman graphs approach. Unitary gauge is used and mass effects are available as well.
Defining equation (physical chemistry) List of equations in classical mechanics; Table of thermodynamic equations; List of equations in wave theory; List of electromagnetism equations; List of relativistic equations; List of equations in fluid mechanics; List of equations in gravitation; List of photonics equations; List of equations in quantum ...
Bargmann–Wigner equations; Schwinger-Dyson equation; Renormalization group equation ... The most famous example of the latter is the phenomenon of Hawking radiation ...
For example, the Aharonov–Bohm effect depends on a line integral of A around a closed loop, and this integral is not changed by +. Gauge fixing in non-abelian gauge theories, such as Yang–Mills theory and general relativity , is a rather more complicated topic; for details see Gribov ambiguity , Faddeev–Popov ghost , and frame bundle .
The Maris-Tandy model can be applied to solve for the structure of pions, kaons, and a selection of vector mesons from the homogeneous Bethe-Salpeter equation [1]. [2] It can also be used to solve for the quark-photon vertex from the inhomogeneous Bethe-Salpeter equation, [3] for the elastic form factors of pseudoscalar mesons, [4] [5] and for the radiative transitions of mesons. [6]
Tomonaga, Schwinger, and Feynman were jointly awarded the 1965 Nobel Prize in Physics for their work in this area. [23] Their contributions, and Dyson's, were about covariant and gauge-invariant formulations of quantum electrodynamics that allow computations of observables at any order of perturbation theory.
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