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The Dyson series, the formal solution of an explicitly time-dependent Schrödinger equation by iteration, and the corresponding Dyson time-ordering operator an entity of basic importance in the mathematical formulation of quantum mechanics, are also named after Dyson.
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Dyson and series
Since then, other variant designs involving building an artificial structure or series of structures to encompass a star have been proposed in exploratory engineering or described in science fiction under the name " Dyson sphere.
The same year, in related work, Dyson invented the Dyson series.
The number of times the interaction Hamiltonian acts is the order of the perturbation expansion, and the time-dependent perturbation theory for fields is known as the Dyson series.
The Dyson series can be alternately rewritten as a sum over Feynman diagrams, where at each interaction vertex both the energy and momentum are conserved, but where the length of the energy momentum four vector is not equal to the mass.
( It is assumed that H does not depend on time and that the perturbation starts at ; otherwise one must use the Dyson series, formally written as
Based on Bethe's intuition and fundamental papers on the subject by Sin-Itiro Tomonaga, Julian Schwinger, Richard Feynman and Freeman Dyson, it was finally possible to get fully covariant formulations that were finite at any order in a perturbation series of quantum electrodynamics.
This series is called the Dyson series.
Using Wick theorem on the terms of the Dyson series, all the terms of the S-matrix for quantum electrodynamics can be computed through the technique of Feynman diagrams.
An argument by Freeman Dyson shows that the radius of convergence of the perturbation series in QED is zero.
Both Dyson spheres and the Ringworld suffer from gravitational instability, however — a major focus of the Ringworld series is coping with this instability in the face of partial collapse of the Ringworld civilization.
* Dyson series
Many further results may be obtained, such as Fermi's golden rule, which relates the rate of transitions between quantum states to the density of states at particular energies, and the Dyson series, obtained by applying the iterative method to the time evolution operator, which is one of the starting points for the method of Feynman diagrams.
Time dependent perturbations can be treated with the technique of Dyson series.
if so that the exponential will represent the following Dyson series
that can be solved through the above Dyson series as
For this purpose, let us write the unitary evolution operator, obtained from the above Dyson series, as
and we consider the question if a dual Dyson series exists that applies in the limit of a perturbation increasingly large.
and we see that the expansion parameter appears only into the exponential and so, the corresponding Dyson series, a dual Dyson series, is meaningful at large s and is
Dyson and formal
Freeman Dyson has shown that these infinities are of a basic nature and cannot be eliminated by any formal mathematical procedures, such as the renormalization method.
Dyson and Schrödinger
Positions regarding existence after death were supported by some notable physicists such as Erwin Schrödinger and Freeman Dyson.
Dyson and equation
Was previously studied by Weyl himself, he developed a method to express the sum as the value, where ' G ' can be defined via a linear differential equation similar to Dyson equation obtained via summation by parts.
the Schwinger – Dyson equation for the generating functional is
The Schwinger – Dyson equation for this particular example is:
* Dyson equation
The Dyson equation relating the full propagator, bare propagator and the 1PI self-energy in the absence of tadpoles
The Dyson equation relates the full propagator, the bare propagator and the 1PI self-energy.
The self-energy operator ( often denoted by, and less frequently by ) is related to the bare and dressed propagators ( often denoted by and respectively ) via the Dyson equation ( named after Freeman John Dyson ):
the resultant equation with the response equation for the physical system yields the Dyson
Dyson and by
* Crank conjecture, a term coined by Freeman Dyson to explain congruence patterns in integer partitions
A Dyson sphere is a hypothetical megastructure originally described by Freeman Dyson.
The concept of the Dyson sphere was the result of a thought experiment by physicist and mathematician Freeman Dyson, when he theorized that all technological civilizations constantly increased their demand for energy.
In response to letters prompted by this paper, Dyson replied, " A solid shell or ring surrounding a star is mechanically impossible.
Dyson is best known for demonstrating in 1949 the equivalence of the formulations of quantum electrodynamics that existed by that time – Richard Feynman's diagrams, on the one hand, and, on the other, the operator method developed by Julian Schwinger and Sin-Itiro Tomonaga.
Robert Oppenheimer, in particular, was persuaded by Dyson that Feynman's new theory was as valid as Schwinger's and Tomonaga's.
Dyson recognized the formula as the pair correlation function of the Gaussian unitary ensemble, which has been extensively studied by physicists.
A seminal work by Dyson came in 1966 when, together with Andrew Lenard and independently of Elliott H. Lieb and Walter Thirring, he proved rigorously that the exclusion principle plays the main role in the stability of bulk matter.
Also during the 1970s, Dyson worked on climate studies conducted by the JASON defense advisory group.
, Dyson is the president of the Space Studies Institute, the space research organization founded by Gerard K. O ' Neill.
The general concept of such an energy-transferring shell had been advanced decades earlier by author Olaf Stapledon in his 1937 novel Star Maker, a source that Dyson has credited publicly.
Since originally taking interest in climate studies in the 1970s, Dyson has suggested that carbon dioxide levels in the atmosphere could be controlled by planting fast-growing trees.
Dyson disagrees with the famous remark by his fellow physicist Steven Weinberg that " With or without religion, good people can behave well and bad people can do evil ; but for good people to do evil — that takes religion.
*" The Question of Global Warming ", by Freeman Dyson, June 12, 2008
:* Comments on " The Question of Global Warming ", with a reply by Dyson, September 25, 2008
*" Our Biotech Future ", essay by Freeman Dyson, July 19, 2007
:* Comments on " Our Biotech Future ", with a reply by Dyson, September 27, 2007
:* Another comment on " Our Biotech Future ", with a reply by Dyson, October 11, 2007
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