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Renormalon
In physics, a renormalon (a term suggested by 't Hooft) is a particular source of divergence seen in perturbative approximations to quantum field theories (QFT). When a formally divergent series in a QFT is summed using Borel summation, the associated Borel transform of the series can have singularities as a function of the complex transform parameter. The renormalon is a possible type of singularity arising in this complex ''Borel plane'', and is a counterpart of an instanton singularity. Associated with such singularities, renormalon contributions are discussed in the context of quantum chromodynamics (QCD) and usually have the power-like form \left(\Lambda/Q\right)^p as functions of the momentum Q (here \Lambda is the momentum cut-off). They are cited against the usual logarithmic effects like \ln\left(\Lambda/Q\right). Brief history Perturbation series in quantum field theory are usually divergent as was firstly indicated by Freeman Dyson. According to the Lipatov method, N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Lipatov
Lev Nikolaevich Lipatov (russian: Лев Никола́евич Липа́тов; 2 May 1940, Leningrad – 4 September 2017, Dubna) was a Russian physicist, well known for his contributions to nuclear physics and particle physics. He has been the head of Theoretical Physics Division at St. Petersburg's Nuclear Physics Institute of Russian Academy of Sciences in Gatchina and an Academician of the Russian Academy of Sciences. For the long period he worked with Vladimir Gribov, laying a basis for a field theory description of deep inelastic scattering and annihilation (Gribov-Lipatov evolution equations, later known as DGLAP, 1972). He wrote significant papers of the Pomeranchuk singularity in Quantum chromodynamics (1977) what resulted in deriving the BFKL evolution equation (Balitsky- Fadin- Kuraev-Lipatov), contributed to the study of critical phenomena (semiclassical Lipatov's approximation), the theory of tunnelling and renormalon contribution to effective couplings. He dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Summation
In mathematics, Borel summation is a summation method for divergent series, introduced by . It is particularly useful for summing divergent asymptotic series, and in some sense gives the best possible sum for such series. There are several variations of this method that are also called Borel summation, and a generalization of it called Mittag-Leffler summation. Definition There are (at least) three slightly different methods called Borel summation. They differ in which series they can sum, but are consistent, meaning that if two of the methods sum the same series they give the same answer. Throughout let denote a formal power series :A(z) = \sum_^\infty a_kz^k, and define the Borel transform of to be its equivalent exponential series :\mathcalA(t) \equiv \sum_^\infty \fract^k. Borel's exponential summation method Let denote the partial sum :A_n(z) = \sum_^n a_k z^k. A weak form of Borel's summation method defines the Borel sum of to be : \lim_ e^\sum_^\infty \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerardus 't Hooft
Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions". His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization and the holographic principle. Personal life He is married to Albertha Schik (Betteke) and has two daughters, Saskia and Ellen. Biography Early life Gerard 't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague. He was the middle child of a family of three. He comes from a family of scholars. His great uncle was Nobel prize laureate Frits Zernike, and his grandmother was married to Pieter Nicolaas van Kampen, a professor of zoology at Leiden Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because: * they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and * they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory. Relevant to dynamics, families of instantons permit that instantons, i.e. different critical points of the equation of motion, be related to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freeman Dyson
Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-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. He was Professor Emeritus in the Institute for Advanced Study in Princeton and a member of the Board of Sponsors of the Bulletin of the Atomic Scientists. Dyson originated several concepts that bear his name, such as Dyson's transform, a fundamental technique in additive number theory, which he developed as part of his proof of Mann's theorem; the Dyson tree, a hypothetical genetically engineered plant capable of growing in a comet; the Dyson series, a perturbative series where each term is represented by Feynman diagrams; the Dyson sphere, a thought experiment that attempts to explain how a spacefaring, space-faring civilization would meet its energy requirements with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benny Lautrup
Benny Lautrup (born 25 June 1939) is a professor in theoretical physics at the Niels Bohr Institute at the University of Copenhagen. During his career he has worked at the Nordic Institute for Theoretical Physics (Denmark), Brookhaven National Laboratory (USA), CERN (Switzerland), and the Institut des Hautes Études Scientifiques (France). He is known for his part in the Nakanishi-Lautrup formalism, a concept in relativistic quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and .... He has published the books ''Neural Networks – Computers with Intuition'' with Søren Brunak (original in Danish and also translated into German), and ''Physics of Continuous Matter: Exotic and Everyday Phenomena in the macroscopic World'' in 2005. A second edition of this book was pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Product Expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question. In practical calculations, such as those needed for scattering amplitudes in various collider experiments, the operator product expansion is used in QCD sum rules to combine results from both perturbative and non-perturbative (condensate) calculations. 2D Euclidean quantum field theory In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated to two operators. A Laurent series is a generalization of the Taylor series in that finitely many powers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
