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Bootstrap Model
The term "bootstrap model" is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles. It is a form of S-matrix theory. Overview In the 1960s and '70s, the ever-growing list of strongly interacting particles — mesons and baryons — made it clear to physicists that none of these particles is elementary. Geoffrey Chew and others went so far as to question the distinction between composite and elementary particles, advocating a "nuclear democracy" in which the idea that some particles were more elementary than others was discarded. Instead, they sought to derive as much information as possible about the strong interaction from plausible assumptions about the S-matrix, which describes what happens when particles of any sort collide, an approach advocated by Werner Heisenberg two decades earlier. The reason the program had any hope of success was because of crossin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term ''satisfiable'' is used instead. The syntactic definition states a theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when \varphi, \lnot \varphi \in \langle A \rangle for no formula \varphi. If there e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regge Theory
Regge may refer to * Tullio Regge (1931-2014), Italian physicist, developer of Regge calculus and Regge theory * Regge calculus, formalism for producing simplicial approximations of spacetimes * Regge theory, study of the analytic properties of scattering * 3778 Regge, main-belt asteroid * Regge (river) The Regge rɛɣəis a river in the Netherlands. It is a tributary to the Vecht of Overijssel. The source of the Regge is near the town Goor Goor () is a city about 20 km west of Enschede in the Dutch province of Overijssel. It received c ..., river in Overijssel, the Netherlands {{disambig, surname Surnames of Italian origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Bootstrap
The conformal bootstrap is a non-perturbative mathematical method to constrain and solve Conformal field theory, conformal field theories, i.e. models of particle physics or statistical physics that exhibit similar properties at different levels of resolution. Overview Unlike more traditional techniques of quantum field theory, conformal bootstrap does not use the Lagrangian (field theory), Lagrangian of the theory. Instead, it operates with the general axiomatic parameters, such as the scaling dimensions of the local operators and their operator product expansion coefficients. A key axiom is that the product of local operators must be expressible as a sum over local operators (thus turning the product into an algebra over a field, algebra); the sum must have a non-zero radius of convergence. This leads to decompositions of correlation functions into structure constants and Virasoro conformal block, conformal blocks. The main ideas of the conformal bootstrap were formulated in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley Mandelstam
Stanley Mandelstam (; 12 December 1928 – 23 June 2016) was a South African theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a central tool in the bootstrap program which sought to formulate a consistent theory of infinitely many particle types of increasing spin. Early life Mandelstam was born in Johannesburg, South Africa to a Jewish family.William D. Rubinstein, Michael Jolles, Hilary L. Rubinstein, ''The Palgrave Dictionary of Anglo-Jewish History'', Palgrave Macmillan (2011), p. 110 Work Mandelstam, along with Tullio Regge, did the initial development of the Regge theory of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tullio Regge
Tullio Eugenio Regge (; July 11, 1931 – October 23, 2014) was an Italian theoretical physicist. Biography Regge obtained the ''laurea'' in physics from the University of Turin in 1952 under the direction of Mario Verde and Gleb Wataghin, and a PhD in physics from the University of Rochester in 1957 under the direction of Robert Marshak. From 1958 to 1959 Regge held a post at the Max Planck Institute for Physics where he worked with Werner Heisenberg. In 1961 he was appointed to the chair of Relativity at the University of Turin. He also held an appointment at the Institute for Advanced Study from 1965 to 1979. He was emeritus professor at the Polytechnic University of Turin while contributing work at CERN as a visiting scientist. Regge died on October 23, 2014. He was married to Rosanna Cester, physicist, by whom he had three children: Daniele, Marta and Anna. In 1959, Regge discovered a mathematical property of potential scattering in the Schrödinger equation—that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condescension or oversimplification." The articles in the magazine are freely available to read online. ''Scientific American'', Wired (magazine), ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like ''Spekt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bootstrapping
In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers or a boot hook tool to help pulling the boots on. The saying "to " was already in use during the 19th century as an example of an impossible task. The idiom dates at least to 1834, when it appeared in the ''Workingman's Advocate'': "It is conjectured that Mr. Murphee will now be enabled to hand himself over the Cumberland river or a barn yard fence by the straps of his boots."Jan FreemanBootstraps and Baron Munchausen ''Boston.com'', January 27, 2009 In 1860 it appeared in a comment on philosophy of mind: "The attempt of the mind to analyze itself san effort analogous to one who would lift himself by his own bootstraps." Bootstrap as a metaphor, meaning to better oneself by one's own unaided efforts, was in use in 1922. This metaphor s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gluons
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind quarks together, forming hadrons such as protons and neutrons. Gluons are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics (QCD). Gluons themselves carry the color charge of the strong interaction. This is unlike the photon, which mediates the electromagnetic interaction but lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than quantum electrodynamics (QED). Properties The gluon is a vector boson, which means, like the photon, it has a spin of 1. While massive spin-1 particles have three polarization states, massless gauge bosons like the gluon have only two polarization states because gauge i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quarks
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly observable matter is composed of up quarks, down quarks and electrons. Owing to a phenomenon known as ''color confinement'', quarks are never found in isolation; they can be found only within hadrons, which include baryons (such as protons and neutrons) and mesons, or in quark–gluon plasmas. There is also the theoretical possibility of more exotic phases of quark matter. For this reason, much of what is known about quarks has been drawn from observations of hadrons. Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. They are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as ''fundamental forces'' (elec ... [...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. Althou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gabriele Veneziano
Gabriele Veneziano (; ; born 7 September 1942) is an Italian theoretical physicist widely considered the father of string theory. He has conducted most of his scientific activities at CERN in Geneva, Switzerland, and held the Chair of Elementary Particles, Gravitation and Cosmology at the Collège de France in Paris from 2004 to 2013, until the age of retirement there. Life Gabriele Veneziano was born in Florence. In 1965, he earned his Laurea in Theoretical Physics from the University of Florence under the direction of . He pursued his doctoral studies at the Weizmann Institute of Science in Rehovot, Israel and obtained his PhD in 1967 under the supervision of Hector Rubinstein. During his stay in Israel, he collaborated, among others, with Marco Ademollo (a professor in Florence) and Miguel Virasoro (an Argentinian physicist who later became a professor in Italy). During his years at MIT, he collaborated with many colleagues and primarily with Sergio Fubini (an MIT professor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
