Landau Principle
''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 ...
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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 in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ...
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Lev Landau
Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. 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, 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 equations for ''S'' matrix singularities. He received the 1962 Nobel Prize in Physics for his development of a mathematical theory of superfluidity that accounts for the properties of liquid helium II at a temperature below (). Life Early years Landau was born ...
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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 physicis ...
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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 ...
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Regge Trajectory
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 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 ..., study of the analytic properties of scattering * 3778 Regge, main-belt asteroid * Regge (river), river in Overijssel, the Netherlands {{disambig, surname Surnames of Italian origin ...
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Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the 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 are ''coordinat ...
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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) * The Narrows (other) * Narrowing (other) Narrowing may refer to: *Narrowing (computer science), a type of algorithm for solving equations between symbolic expressions **Narrowing of algebraic value sets, a method for the elimination of values from a solution set which are inconsistent wit ...

Regge Trajectories
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 ...

Kramers–Kronig Relations
The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane. The relations are often used to compute the real part from the imaginary part (or vice versa) of response functions in physical systems, because for stable systems, causality implies the condition of 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) are real. Suppose this function is analytic in the closed upper half-plane of \omega and vanishes faster than 1/, \omega, as , \omega, \to \infty. Slightly weaker conditi ...
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Dispersion Relations
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the phase velocity and group velocity of waves in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency dependence of wave propagation and attenuation. Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase vel ...
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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 an infinite series representation in terms of which it is initially defined 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 ...
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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 ...
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