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Veneziano Scattering Amplitude
In theoretical physics, the Veneziano amplitude refers to the discovery made in 1968 by Italian theoretical physicist Gabriele Veneziano that the Euler beta function, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality. Conformal symmetry was soon discovered. This discovery can be considered the birth of string theory, as the discovery and invention of string theory came about as a search for a physical model which would give rise to such a scattering amplitude. In particular, the amplitude appears as the four tachyon scattering amplitude in orientated open bosonic string theory. Using Mandelstam variables and the beta function B(x,y), the amplitude is given by : S(k_1,k_2,k_3,k_4) = \frac(2\pi)^\delta^(\Sigma_i k_i)\big (\alpha(s),\alpha(t))+B(\alpha(s),\alpha(u))+B(\alpha(t),\alpha(u))\big where \alpha' is the string constant, k_i are the tachyon four-vectors, ... [...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 concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bosonic String Theory
Bosonic string theory is the original version of string theory, developed in the late 1960s and named after Satyendra Nath Bose. It is so called because it contains only bosons in the spectrum. In the 1980s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful model to understand many general features of perturbative string theory, and many theoretical difficulties of superstrings can actually already be found in the context of bosonic strings. Problems Although bosonic string theory has many attractive features, it falls short as a viable physical model in two significant areas. First, it predicts only the existence of bosons whereas many physical particles are fermions. Second, it predicts the existence of a mode of the string with imaginary mass, implying that the theory has an instability t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicist, who is a professor of theoretical physics at Stanford University, and founding director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study. Susskind is widely regarded as one of the fathers of string theory. He was the first to give a precise string-theoretic interpretation of the holographic principle in 1995 and the first to introduce the idea of the stri ... [...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] |
History Of String Theory
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics. 1943–1959: S-matrix theory String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. The field became marginalized and discarded in the mid 1970s and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and because quantum chromodynamics supplanted it as an experimentally better-qualified approach to the strong interactions. The theory presented a radical rethi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Resonance Model
In theoretical physics, a dual resonance model arose during the early investigation (1968–1973) of string theory as an S-matrix theory of the strong interaction. Overview The dual resonance model was based upon the observation that the amplitudes for the s-channel scatterings matched exactly with the amplitudes for the t-channel scatterings among mesons and also the Regge trajectory. It began with the Euler beta function model of Gabriele Veneziano in 1968 for a 4-particle amplitude which has the property that it is explicitly s–t crossing symmetric, exhibits duality between the description in terms of Regge poles or of resonances, and provides a closed-form solution to non-linear finite-energy sum rules relating s- and t- channels. The Veneziano formula was quickly generalized to an equally consistent ''N''-particle amplitude for which Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind provided a physical interpretation in terms of an infinite number of simple harm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossing (physics)
In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time. Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle \mathrm to scatter with \mathrm and produce particle \mathrm and \mathrm will also give the scattering amplitude for \scriptstyle \mathrm+\bar+\mathrm to go into \mathrm, or for \scriptstyle \bar to scatter with \scriptstyle \mathrm to produce \scriptstyle \mathrm+\bar. The only difference is that the value of the energy is negative for the antiparticle. The formal way to state this property is that the antiparticle scattering amplitudes are the analytic continuation of particle scattering amplitudes to negative energies. The interpretation of this statement is that the antiparticle is in every way a particle going backwards in time. History Murray Gell-Mann and Marvin Leonard Gol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-vector
In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (,) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). Four-vectors describe, for instance, position in spacetime modeled as Minkowski space, a particle's four-momentum , the amplitude of the electromagnetic four-potential at a point in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra. The Lorentz group may be represented by 4×4 matrices . The action of a Lorentz transformation o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandelstam Variables
In theoretical physics, the Mandelstam variables are numerical quantities that encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. They are used for scattering processes of two particles to two particles. The Mandelstam variables were first introduced by physicist Stanley Mandelstam in 1958. If the Minkowski metric is chosen to be \mathrm(1, -1,-1,-1), the Mandelstam variables s,t,u are then defined by :*s=(p_1+p_2)^2 c^2 =(p_3+p_4)^2 c^2 :*t=(p_1-p_3)^2 c^2 =(p_4-p_2)^2 c^2 :*u=(p_1-p_4)^2 c^2 =(p_3-p_2)^2 c^2, where ''p''1 and ''p''2 are the four-momenta of the incoming particles and ''p''3 and ''p''4 are the four-momenta of the outgoing particles. s is also known as the square of the center-of-mass energy ( invariant mass) and t as the square of the four-momentum transfer. Feynman diagrams The letters ''s,t,u'' are also used in the terms s-channel (timelike channel), t-channel, and u-channel (both spacelike channels) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Physics
''Lecture Notes in Physics'' (LNP) is a book series published by Springer Science+Business Media in the field of physics, including articles related to both research and teaching. It was established in 1969. See also * ''Lecture Notes in Computer Science'' * ''Lecture Notes in Mathematics ''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Sp ...'' External links * Publications established in 1969 Physics books Series of books Springer Science+Business Media books {{physics-book-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical region. Italy is also considered part of Western Europe, and shares land borders with France, Switzerland, Austria, Slovenia and the enclaved microstates of Vatican City and San Marino. It has a territorial exclave in Switzerland, Campione. Italy covers an area of , with a population of over 60 million. It is the third-most populous member state of the European Union, the sixth-most populous country in Europe, and the tenth-largest country in the continent by land area. Italy's capital and largest city is Rome. Italy was the native place of many civilizations such as the Italic peoples and the Etruscans, while due to its central geographic location in Southern Europe and the Mediterranean, the country has also historically been home ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer (publisher)
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
