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There are some review article about applications of the Schwinger–Dyson equations with applications to special field of physics. For applications to Quantum Chromodynamics there are R. Alkofer and L. v.Smekal (2001). "On the infrared behaviour of QCD Green's functions". Phys. Rep. 353 (5– 6): 281. arXiv: hep-ph/0007355. Bibcode:2001PhR ...
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.
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 .
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 ...
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.
The Dyson V8 is a powerhouse of a vacuum; it’s cordless and features a detachable handle that acts as a second, smaller vacuum perfect for corners or places that are harder to reach with a floor ...
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 ...
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.