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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 quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators.
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]
[citation needed] Most recently, [specify] Lee and Richard M. Friedberg developed a new method to solve the Schrödinger equation, leading to convergent iterative solutions for the long-standing quantum degenerate double-wall potential and other instanton problems. They also did work on the neutrino mapping matrix.
These directly corresponded (through the Schwinger–Dyson equation) to the measurable physical processes (cross sections, probability amplitudes, decay widths and lifetimes of excited states) one needs to be able to calculate. This revolutionized how quantum field theory calculations are carried out in practice.
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.
In fact, since the propagator is obtained by inverting the wave equation, in general, it will have singularities on shell. The energy carried by the particle in the propagator can even be negative . This can be interpreted simply as the case in which, instead of a particle going one way, its antiparticle is going the other way, and therefore ...