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Renormalization Group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to ''scale invariance'' and ''conformal invariance'', symmetries in which a system appears the same at all scales (so-called self-similarity). As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Background Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and elasticity), thermal, electrical, magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern ( crystalline solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Function (physics)
In theoretical physics, specifically quantum field theory, a beta function, ''β(g)'', encodes the dependence of a coupling parameter, ''g'', on the energy scale, ''μ'', of a given physical process described by quantum field theory. It is defined as :: \beta(g) = \frac ~, and, because of the underlying renormalization group, it has no explicit dependence on ''μ'', so it only depends on ''μ'' implicitly through ''g''. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques. Scale invariance If the beta functions of a quantum field theory vanish, usually at particular values of the coupling parameters, then the theory is said to be scale-invariant. Almost all scale-invariant QFTs are also conformally invariant. The study of such theories is conformal field theory. The cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schröder's Equation
Schröder's equation, named after Ernst Schröder, is a functional equation with one independent variable: given the function , find the function such that Schröder's equation is an eigenvalue equation for the composition operator that sends a function to . If is a fixed point of , meaning , then either (or ) or . Thus, provided that is finite and does not vanish or diverge, the eigenvalue is given by . Functional significance For , if is analytic on the unit disk, fixes , and , then Gabriel Koenigs showed in 1884 that there is an analytic (non-trivial) satisfying Schröder's equation. This is one of the first steps in a long line of theorems fruitful for understanding composition operators on analytic function spaces, cf. Koenigs function. Equations such as Schröder's are suitable to encoding self-similarity, and have thus been extensively utilized in studies of nonlinear dynamics (often referred to colloquially as chaos theory). It is also used in studies of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Wegner
Franz Joachim Wegner (born 15 June 1940) is emeritus professor for theoretical physics at the University of Heidelberg. Education Franz Wegner attained a doctorate in 1968 with thesis advisor Wilhelm Brenig at the Technical University Munich with the thesis, "Zum Heisenberg-Modell im paramagnetischen Bereich und am kritischen Punkt" ("On the Heisenberg model within the paramagnetic range and at the critical point"). Subsequently, he did research with a post-doctoral position at Forschungszentrum Jülich, in the group of Herbert Wagner and at Brown University with Leo Kadanoff. Since 1974 he is a professor at Heidelberg.. Research The emphasis of Wegner's scientific work is statistical physics, in particular the theory of phase transitions and the renormalization group. The eponymous "Wegner exponent" is of fundamental importance for the purpose of describing corrections to asymptotic scale invariance in close proximity to phase transitions. Wegner also "invented" the foundatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis E
Francis may refer to: People *Pope Francis, the head of the Catholic Church and sovereign of the Vatican City State and Bishop of Rome * Francis (given name), including a list of people and fictional characters * Francis (surname) Places *Rural Municipality of Francis No. 127, Saskatchewan, Canada *Francis, Saskatchewan, Canada ** Francis (electoral district) * Francis, Nebraska * Francis Township, Holt County, Nebraska *Francis, Oklahoma * Francis, Utah Other uses * ''Francis'' (film), the first of a series of comedies featuring Francis the Talking Mule, voiced by Chill Wills *''Francis'', a 1983 play by Julian Mitchell *FRANCIS, a bibliographic database * ''Francis'' (1793), a colonial schooner in Australia * Francis turbine, a type of water turbine * Francis (band), a Sweden-based folk band * Francis, a character played by YouTuber Boogie2988 See also *Saint Francis (other) St. Francis or Saint Francis may refer to: Roman Catholic saints *Francis of Assisi (1181â ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murray Gell-Mann
Murray Gell-Mann (; September 15, 1929 – May 24, 2019) was an American physicist who received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. He was the Robert Andrews Millikan Professor of Theoretical Physics Emeritus at the California Institute of Technology, a distinguished fellow and one of the co-founders of the Santa Fe Institute, a professor of physics at the University of New Mexico, and the Presidential Professor of Physics and Medicine at the University of Southern California. Gell-Mann spent several periods at CERN, a nuclear research facility in Switzerland, among others as a John Simon Guggenheim Memorial Foundation fellow in 1972. Early life and education Gell-Mann was born in Lower Manhattan to a family of Jewish immigrants from the Austro-Hungarian Empire, specifically from Czernowitz in present-day Ukraine. His parents were Pauline (née Reichstein) and Arthur Isidore Gell-Mann, who taught English as a second language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta-function
In theoretical physics, specifically quantum field theory, a beta function, ''β(g)'', encodes the dependence of a coupling parameter, ''g'', on the energy scale, ''μ'', of a given physical process described by quantum field theory. It is defined as :: \beta(g) = \frac ~, and, because of the underlying renormalization group, it has no explicit dependence on ''μ'', so it only depends on ''μ'' implicitly through ''g''. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques. Scale invariance If the beta functions of a quantum field theory vanish, usually at particular values of the coupling parameters, then the theory is said to be scale-invariant. Almost all scale-invariant QFTs are also conformally invariant. The study of such theories is conformal field theory. The coup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
André Petermann
Andreas Emil Petermann (27 September 1922, Lausanne, Switzerland – 21 August 2011, Lausanne), known as André Petermann, was a Swiss theoretical physicist known for introducing the renormalization group, suggesting a quark-like model, and work related to the anomalous magnetic dipole moment of the muon. Petermann obtained his doctorate from the University of Lausanne in May 1952 under the supervision of professor Ernst Stueckelberg. The work was funded by the Swiss Atomic Energy Commission. Following Lausanne, Petermann moved on to the University of Manchester, UK, before he became a CERN staff member in 1955. The CERN Theory Division was at that time still hosted at the University of Copenhagen. It was then moved to Geneva together with the CERN experimental groups in 1957. Work Jointly with his advisor, Ernst Stueckelberg, in 1953, they introduced, and named the "renormalization group", which describes the running of physical couplings with energy. He also, apparently indep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Stueckelberg
Ernst Carl Gerlach Stueckelberg (baptised as Johann Melchior Ernst Karl Gerlach Stückelberg, full name after 1911: Baron Ernst Carl Gerlach Stueckelberg von Breidenbach zu Breidenstein und Melsbach; 1 February 1905 – 4 September 1984) was a Swiss mathematician and physicist, regarded as one of the most eminent physicists of the 20th century. Despite making key advances in theoretical physics, including the exchange particle model of fundamental forces, causal S-matrix theory, and the renormalization group, his idiosyncratic style and publication in minor journals led to his work not being widely recognized until the mid-1990s. Early life Born into a semi-aristocratic family in Basel in 1905, Stueckelberg's father was a lawyer, and his paternal grandfather a distinguished Swiss artist. A highly gifted school student, Stueckelberg initially began a physics degree at the University of Basel in 1923. Career While still a student, Stueckelberg was invited by the distinguished qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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