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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.
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 ...
Freeman John Dyson FRS (15 December 1923 – 28 February 2020) [1] was a British-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum mechanics, condensed matter physics, nuclear physics, and engineering.
Ordinary quantum field theories, which form the basis of standard model, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth.
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism.They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics.
Standard Model of Particle Physics. The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces.