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S-matrix Theory
''S''-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics. It avoided the notion of space and time by replacing it with abstract mathematical properties of the ''S''-matrix. In ''S''-matrix theory, the ''S''-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices. This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory, which was plagued with the zero interaction phenomenon at strong coupling. Applied to the strong interaction, it led to the development of string theory. ''S''-matrix theory was largely abandoned by physicists in the 1970s, as quantum chromodynamics was recognized to solve the problems of strong interactions within the framework of field theory. But in the guise of string theory, ''S''-matrix theory is still a popular approach to the problem of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Landau
Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and made seminal contributions to all branches of physics. He is credited with laying the foundations of twentieth century condensed matter physics, and is also considered arguably the greatest Soviet theoretical physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, invention of order parameter technique, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pomeron
In physics, the pomeron is a Regge trajectory — a family of particles with increasing spin — postulated in 1961 to explain the slowly rising cross section of hadronic collisions at high energies. It is named after Isaak Pomeranchuk. Overview While other trajectories lead to falling cross sections, the pomeron can lead to logarithmically rising cross sections — which, experimentally, are approximately constant ones. The identification of the pomeron and the prediction of its properties was a major success of the Regge theory of strong interaction phenomenology. In later years, a BFKL pomeron was derived in further kinematic regimes from perturbative calculations in QCD, but its relationship to the pomeron seen in soft high energy scattering is still not fully understood. One consequence of the pomeron hypothesis is that the cross sections of proton–proton and proton–antiproton scattering should be equal at high enough energies. This was demonstrated by the Soviet ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 cross ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regge Trajectory
In quantum physics, Regge theory ( , ) is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer multiple of '' ħ'' but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1959. Details The simplest example of Regge poles is provided by the quantum mechanical treatment of the Coulomb potential V(r) = -e^2/(4\pi\epsilon_0r) or, phrased differently, by the quantum mechanical treatment of the binding or scattering of an electron of mass m and electric charge -e off a proton of mass M and charge +e. The energy E of the binding of the electron to the proton is negative whereas for scattering the energy is positive. The formula for the binding energy is the expression :E\rightarrow E_N = - \frac = - \frac, \;\;\; m^' = \frac, where N = 1,2,3,..., h is the Planck constant, and \epsilon_0 is the permittivity of the vacuum. The principal quantum numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Narrow Resonance Approximation
Narrow may refer to: * The Narrow, rock band from South Africa * Narrow banking, proposed banking system that would eliminate bank runs and the need for a deposit insurance * Narrow-gauge railway, a railway that has a track gauge narrower than the 4 ft 8½ in of standard gauge railways * Narrow vs wide format, a style of displaying tabular data * Narrowboat or narrow boat, a boat of a distinctive design made to fit the narrow canals of Great Britain * ''Narrow'' (album), a 2012 album by Austrian musical project Soap&Skin * "Narrow", a song by Mayday Parade from ''Black Lines'' See also * Narro (other) * Narrows (other) * The Narrows (other) The Narrows is a strait in New York City separating Brooklyn and Staten Island. The Narrows may also refer to: Places Antarctica * The Narrows (Antarctica), a strait Australia * The Narrows (Victoria), a strait of the Western Port Bay between t ... * Narrowing (other) * * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regge Trajectories
In quantum physics, Regge theory ( , ) is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer multiple of '' ħ'' but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1959. Details The simplest example of Regge poles is provided by the quantum mechanical treatment of the Coulomb potential V(r) = -e^2/(4\pi\epsilon_0r) or, phrased differently, by the quantum mechanical treatment of the binding or scattering of an electron of mass m and electric charge -e off a proton of mass M and charge +e. The energy E of the binding of the electron to the proton is negative whereas for scattering the energy is positive. The formula for the binding energy is the expression :E\rightarrow E_N = - \frac = - \frac, \;\;\; m^' = \frac, where N = 1,2,3,..., h is the Planck constant, and \epsilon_0 is the permittivity of the vacuum. The principal quantum numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kramers–Kronig Relations
The Kramers–Kronig relations, sometimes abbreviated as KK relations, are bidirectional mathematics, mathematical relations, connecting the real number, real and imaginary number, imaginary parts of any complex analysis, complex function that is analytic function, analytic in the upper half-plane. The relations are often used to compute the real part from the imaginary part (or vice versa) of linear response function, response functions in physical systems, because for stable systems, causal system, causality implies the condition of Analytic function, analyticity, and conversely, analyticity implies causality of the corresponding stable physical system. The relation is named in honor of Ralph Kronig and Hans Kramers. In mathematics, these relations are known by the names Sokhotski–Plemelj theorem and Hilbert transform. Formulation Let \chi(\omega) = \chi_1(\omega) + i \chi_2(\omega) be a complex function of the complex variable \omega, where \chi_1(\omega) and \chi_2(\omega) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes divergent. The step-wise continuation technique may, however, come up against difficulties. These may have an essentially topological nature, leading to inconsistencies (defining more than one value). They may alternatively have to do with the presence of singularities. The case of several complex variables is rather different, since singularities then need not be isolated points, and its investigation was a major reason for the development of sheaf cohomology. Initial discussion Suppose ''f'' is an analytic function defined on a non-empty open subset ''U'' of the complex plane If ''V'' is a larger open subset of containing ''U'', and ... [...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 \mathrm+\bar+\mathrm to go into \mathrm, or for \bar to scatter with \mathrm to produce \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 Goldberger introduced crossing symmetry in 1954. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitarity
In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum mechanics, while generalizations of or departures from unitarity are part of speculations about theories that may go beyond quantum mechanics. A unitarity bound is any inequality that follows from the unitarity of the evolution operator, i.e. from the statement that time evolution preserves inner products in Hilbert space. Hamiltonian evolution Time evolution described by a time-independent Hamiltonian is represented by a one-parameter family of unitary operators, for which the Hamiltonian is a generator: U(t) = e^. In the Schrödinger picture, the unitary operators are taken to act upon the system's quantum state, whereas in the Heisenberg picture, the time dependence is incorporated into the observables in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
