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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 ...
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'ichirō Tomonaga and Julian Schwinger appreciated that covariant perturbation ...
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 ...
Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. Using the well-known observation that = ()!, Julian Schwinger noticed that one may simplify the integral:
The Lippmann–Schwinger equation for the scattering state | with a momentum p and out-going (+) or in-going (−) boundary conditions is | = | + | , where is the free particle Green's function, is a positive infinitesimal quantity, and the interaction potential.
Dyson originated several concepts that bear his name, such as Dyson's transform, a fundamental technique in additive number theory, [5] which he developed as part of his proof of Mann's theorem; [6] the Dyson tree, a hypothetical genetically engineered plant capable of growing in a comet; the Dyson series, a perturbative series where each term ...
It is also referred to as the Sauter–Schwinger effect, Schwinger mechanism, or Schwinger pair production. It is a prediction of quantum electrodynamics (QED) in which electron – positron pairs are spontaneously created in the presence of an electric field, thereby causing the decay of the electric field.