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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'ichirō 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.
The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using the Dyson series. It should be observed that the decomposition into free fields and interactions is in principle arbitrary.
In 1941, Rarita and Schwinger focussed on spin-3 ⁄ 2 particles and derived the Rarita–Schwinger equation, including a Lagrangian to generate it, and later generalized the equations analogous to spin n + 1 ⁄ 2 for integer n. In 1945, Pauli suggested Majorana's 1932 paper to Bhabha, who returned to the general ideas introduced by Majorana ...
In quantum field theory, an operator valued distribution is a free field if it satisfies some linear partial differential equations such that the corresponding case of the same linear PDEs for a classical field (i.e. not an operator) would be the Euler–Lagrange equation for some quadratic Lagrangian.