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Higher-spin Theory
Higher-spin theory or higher-spin gravity is a common name for field theories that contain massless fields of spin greater than two. Usually, the spectrum of such theories contains the graviton as a massless spin-two field, which explains the second name. Massless fields are gauge fields and the theories should be (almost) completely fixed by these higher-spin symmetries. Higher-spin theories are supposed to be consistent quantum theories and, for this reason, to give examples of quantum gravity. Most of the interest in the topic is due to the AdS/CFT correspondence where there is a number of conjectures relating higher-spin theories to weakly coupled conformal field theories. It is important to note that only certain parts of these theories are known at present (in particular, standard action principles are not known) and not many examples have been worked out in detail except some specific toy models (such as the higher-spin extension of pure Chern–Simons, Jackiw–Teitelboim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field Theory (physics)
In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. An example of a scalar field is a weather map, with the surface temperature described by assigning a number to each point on the map. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field. In the modern framework of the quantum field theory, even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical "true vacuum". ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Juan Martín Maldacena
Juan Martín Maldacena (; born 10 September 1968) is an Argentine theoretical physicist and the Carl P. Feinberg Professor in the School of Natural Sciences at the Institute for Advanced Study, Princeton. He has made significant contributions to the foundations of string theory and quantum gravity. His most famous discovery is the AdS/CFT correspondence, a realization of the holographic principle in string theory. Biography Maldacena obtained his ''licenciatura'' (a six-year degree) in 1991 at the Instituto Balseiro, Bariloche, Argentina, under the supervision of Gerardo Aldazábal. He then obtained his Ph.D. in physics at Princeton University after completing a doctoral dissertation titled "Black holes in string theory" under the supervision of Curtis Callan in 1996, and went on to a post-doctoral position at Rutgers University. In 1997, he joined Harvard University as associate professor, being quickly promoted to Professor of Physics in 1999. Since 2001 he has been a pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bargmann–Wigner Equations
In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles with non-zero mass and arbitrary spin , an integer for bosons () or half-integer for fermions (). The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields. They are named after Valentine Bargmann and Eugene Wigner. History Paul Dirac first published the Dirac equation in 1928, and later (1936) extended it to particles of any half-integer spin before Fierz and Pauli subsequently found the same equations in 1939, and about a decade before Bargman, and Wigner. Eugene Wigner wrote a paper in 1937 about unitary representations of the inhomogeneous Lorentz group, or the Poincaré group. Wigner notes Ettore Majorana and Dirac used infinitesimal operators applied to functions. Wigner classifies representations as irreducible, factorial, and unitary. In 1948 Valentine Bargmann and Wigner published the equations now na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vasiliev Equations
Vasiliev equations are ''formally'' consistent gauge invariant nonlinear equations whose linearization over a specific vacuum solution describes free massless higher-spin fields on anti-de Sitter space. The Vasiliev equations are classical equations and no Lagrangian is known that starts from canonical two-derivative Frønsdal Lagrangian and is completed by interactions terms. There is a number of variations of Vasiliev equations that work in three, four and arbitrary number of space-time dimensions. Vasiliev's equations admit supersymmetric extensions with any number of super-symmetries and allow for Yang–Mills gaugings. Vasiliev's equations are background independent, the simplest exact solution being anti-de Sitter space. It is important to note that locality is not properly implemented and the equations give a solution of certain formal deformation procedure, which is difficult to map to field theory language. The higher-spin AdS/CFT correspondence is reviewed in Higher-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
W-algebra
In conformal field theory and representation theory, a W-algebra is an associative algebra that generalizes the Virasoro algebra. W-algebras were introduced by Alexander Zamolodchikov, and the name "W-algebra" comes from the fact that Zamolodchikov used the letter W for one of the elements of one of his examples. Definition A W-algebra is an associative algebra that is generated by the modes of a finite number of meromorphic fields W^(z), including the energy-momentum tensor T(z)=W^(z). For h\neq 2, W^(z) is a primary field of conformal dimension h\in\frac12\mathbb^*. The generators (W^_n)_ of the algebra are related to the meromorphic fields by the mode expansions : W^(z) = \sum_ W^_n z^ The commutation relations of L_n=W^_n are given by the Virasoro algebra, which is parameterized by a central charge c\in \mathbb. This number is also called the central charge of the W-algebra. The commutation relations : _m, W^_n= ((h-1)m-n)W^_ are equivalent to the assumption that W^(z) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers defined from the sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon or , or less commonly the Latin lower case . Index notation allows one to display permutations in a way compatible with tensor analysis: \varepsilon_ where ''each'' index takes values . There are indexed values of , which can be arranged into an -dimensional array. The key defining property of the symbol is ''total antisymmetry'' in the indices. When any two indices are interchanged, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Connection
In differential geometry and mathematical physics, a spin connection is a connection (vector bundle), connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection. It can also be regarded as the gauge field generated by local Lorentz transformations. In some canonical formulations of general relativity, a spin connection is defined on spatial slices and can also be regarded as the gauge field generated by local rotations. The spin connection occurs in two common forms: the ''Levi-Civita spin connection'', when it is derived from the Levi-Civita connection, and the ''affine spin connection'', when it is obtained from the affine connection. The difference between the two of these is that the Levi-Civita connection is by definition the unique torsion tensor, torsion-free connection, whereas the affine connection (and so the affine spin connection) may contain torsion. Definition Let e_\mu^ be the local Lorentz frame fields or Cartan formalism (phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weyl Transformation
In theoretical physics, the Weyl transformation, named after German mathematician Hermann Weyl, is a local rescaling of the metric tensor: g_ \rightarrow e^ g_ which produces another metric in the same conformal class. A theory or an expression invariant under this transformation is called conformally invariant, or is said to possess Weyl invariance or Weyl symmetry. The Weyl symmetry is an important symmetry in conformal field theory. It is, for example, a symmetry of the Polyakov action. When quantum mechanical effects break the conformal invariance of a theory, it is said to exhibit a conformal anomaly or Weyl anomaly. The ordinary Levi-Civita connection and associated spin connections are not invariant under Weyl transformations. Weyl connections are a class of affine connections that is invariant, although no Weyl connection is individual invariant under Weyl transformations. Conformal weight A quantity \varphi has conformal weight k if, under the Weyl transforma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Gravity
Conformal gravity refers to gravity theories that are invariant under conformal transformations in the Riemannian geometry sense; more accurately, they are invariant under Weyl transformations g_\rightarrow\Omega^2(x)g_ where g_ is the metric tensor and \Omega(x) is a function on spacetime. Weyl-squared theories The simplest theory in this category has the square of the Weyl tensor as the Lagrangian :\mathcal=\int \, \mathrm^4x \, \sqrt \, C_\,C^~, where \; C_ \; is the Weyl tensor. This is to be contrasted with the usual Einstein–Hilbert action where the Lagrangian is just the Ricci scalar. The equation of motion upon varying the metric is called the Bach tensor, :2\,\partial_a\,\partial_d\,^d ~~+~~ R_ \, ^d ~=~ 0~, where \; R_ \; is the Ricci tensor. Conformally flat metrics are solutions of this equation. Since these theories lead to fourth-order equations for the fluctuations around a fixed background, they are not manifestly unitary. It has therefore been genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein–Hilbert Action
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the metric signature, the gravitational part of the action is given as :S = \int R \sqrt \, \mathrm^4x, where g=\det(g_) is the determinant of the metric tensor matrix, R is the Ricci scalar, and \kappa = 8\pi Gc^ is the Einstein gravitational constant (G is the gravitational constant and c is the speed of light in vacuum). If it converges, the integral is taken over the whole spacetime. If it does not converge, S is no longer well-defined, but a modified definition where one integrates over arbitrarily large, relatively compact domains, still yields the Einstein equation as the Euler–Lagrange equation of the Einstein–Hilbert action. The action was proposed by David Hilbert in 1915 as part of his application of the variational principle to a combination of gravity and electromagnetism. Discussion Deriving equations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck Length
In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature (specifically, properties of free space) rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity. The term Planck scale refers to quantities of space, time, energy and other units that are similar in magnitude to corresponding Planck units. This region may be characterized by particle energies of around or , time intervals of around and lengths of around (approximately the energy-equivalent of the Planck mass, the Planck time and the Planck len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No-go Theorems
In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. This type of theorem imposes boundaries on certain mathematical or physical possibilities via a proof by contradiction. Instances of no-go theorems Full descriptions of the no-go theorems named below are given in other articles linked to their names. A few of them are broad, general categories under which several theorems fall. Other names are broad and general-sounding but only refer to a single theorem. Classical electrodynamics * Antidynamo theorems are a general category of theorems that restrict the type of magnetic fields that can be produced by dynamo theory, dynamo action. * Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary mechanical equilibrium, equilibrium configuration solely by the electrostatic interaction of the charges. Non-relativistic quantum mechanics and quantum information * Bell's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
