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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 .
Dyson was elected to the United States National Academy of Sciences in 1964. [95] Dyson was awarded the Dannie Heineman Prize for Mathematical Physics in 1965, Lorentz Medal in 1966, Max Planck Medal in 1969, the J. Robert Oppenheimer Memorial Prize in 1970, [96] [97] the Harvey Prize in 1977 [98] and Wolf Prize in 1981. [99]
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.
By utilizing the interaction picture, one can use time-dependent perturbation theory to find the effect of H 1,I, [15]: 355ff e.g., in the derivation of Fermi's golden rule, [15]: 359–363 or the Dyson series [15]: 355–357 in quantum field theory: in 1947, Shin'ichirÅ Tomonaga and Julian Schwinger appreciated that covariant perturbation ...
Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions.
The starting point for the derivation of the Bethe–Salpeter equation is the two-particle (or four point) Dyson equation = + in momentum space, where "G" is the two-particle Green function | | , "S" are the free propagators and "K" is an interaction kernel, which contains all possible interactions between the two particles.
This gives rise to an infinite chain of coupled equations for different Wilson loop expectation values, analogous to the Schwinger–Dyson equations. The Makeenko–Migdal equation has been solved exactly in two dimensional U ( ∞ ) {\displaystyle {\text{U}}(\infty )} theory.