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Meron (physics)
A meron or half-instanton is a Euclidean space-time solution of the Yang–Mills field equations. It is a singular non-self-dual solution of topological charge 1/2. The instanton is believed to be composed of two merons. A meron can be viewed as a tunneling event between two Gribov vacua. In that picture, the meron is an event which starts from vacuum, then a Wu–Yang monopole emerges, which then disappears again to leave the vacuum in another Gribov copy. See also *BPST instanton *Dyon *Instanton * Monopole *Sphaleron References * ''Gauge Fields, Classification and Equations of Motion'', Moshe Carmeli, Kh. Huleilil and Elhanan Leibowitz, World Scientific Publishing World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, with more than 170 journals in var ... Gauge theories Quantum chromodynamics {{quantum-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces'' of any positive integer dimension ''n'', which are called Euclidean ''n''-spaces when one wants to specify their dimension. For ''n'' equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of '' proving'' all properties of the space as theorems, by starting from a few fundamental properties, called '' postulates'', which either were considered as evid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solution (equation)
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as '' unknowns''. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality. A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation ''numerically'' means that only numbers are admitted as solutions. Solving an equation ''symbolically'' means that expressions can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Theory
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, the Lagrangian is invariant under these transformations. The term "gauge" refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the '' symmetry group'' or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BPST Instanton
In theoretical physics, the BPST instanton is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu. S. Tyupkin. It is a classical solution to the equations of motion of SU(2) Yang–Mills theory in Euclidean space-time (i.e. after Wick rotation), meaning it describes a transition between two different topological vacua of the theory. It was originally hoped to open the path to solving the problem of confinement, especially since Polyakov had proven in 1975 that instantons are the cause of confinement in three-dimensional compact-QED. This hope was not realized, however. Description The instanton The BPST instanton is an essentially non-perturbative classical solution of the Yang–Mills field equations. It is found when minimizing the Yang–Mills SU(2) Lagrangian density: :\mathcal L = -\frac14F_^a F_^a with ''F''μν''a'' = ∂μ''A''ν''a'' – ∂ν''A''μ''a'' + ''g''ε''abc''''A''μ''b''''A''ν''c'' the field stren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Tunnelling
In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier. Tunneling is a consequence of the wave nature of matter, where the quantum wave function describes the state of a particle or other physical system, and wave equations such as the Schrödinger equation describe their behavior. The probability of transmission of a wave packet through a barrier decreases exponentially with the barrier height, the barrier width, and the tunneling particle's mass, so tunneling is seen most prominently in low-mass particles such as electrons or protons tunneling through microscopically narrow barriers. Tunneling is readily detectable with barriers of thickness about 1–3 nm or smaller for electrons, and abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gribov Ambiguity
In gauge theory, especially in non-abelian gauge theories, global problems at gauge fixing are often encountered. Gauge fixing means choosing a representative from each gauge orbit, that is, choosing a section of a fiber bundle. The space of representatives is a submanifold (of the bundle as a whole) and represents the gauge fixing condition. Ideally, every gauge orbit will intersect this submanifold once and only once. Unfortunately, this is often impossible globally for non-abelian gauge theories because of topological obstructions and the best that can be done is make this condition true locally. A gauge fixing submanifold may not intersect a gauge orbit at all or it may intersect it more than once. The difficulty arises because the gauge fixing condition is usually specified as a differential equation of some sort, e.g. that a divergence vanish (as in the Landau or Lorenz gauge). The solutions to this equation may end up specifying multiple sections, or perhaps none at all. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reviews Of Modern Physics
''Reviews of Modern Physics'' (often abbreviated RMP) is a quarterly Peer review, peer-reviewed scientific journal published by the American Physical Society. It was established in 1929 and the current editor-in-chief is Michael Thoennessen. The journal publishes review articles, usually by established researchers, on all aspects of physics and related fields. The reviews are usually accessible to non-specialists and serve as introductory material to graduate students, which survey recent work, discuss key problems to be solved and provide perspectives toward the end. The journal has published several historically significant papers on quantum foundations, as well as the development of the Standard Model of particle physics. References External links * Academic journals established in 1929 Physics review journals Quarterly journals English-language journals American Physical Society academic journals {{physics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wu–Yang Monopole
The Wu–Yang monopole was the first solution (found in 1968 by Tai Tsun Wu and Chen Ning YangWu, T.T. and Yang, C.N. (1968) in ''Properties of Matter Under Unusual Conditions'', edited by H. Mark and S. Fernbach (Interscience, New York)) to the Yang–Mills field equations. It describes a magnetic monopole which is pointlike and has a potential which behaves like 1/''r'' everywhere. See also * Meron * Dyon *Instanton An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. M ... * Wu–Yang dictionary Notes References * ''Gauge Fields, Classification and Equations of Motion'', M.Carmeli, Kh. Huleilil and E. Leibowitz, World Scientific Publishing * Gauge theories Magnetic monopoles {{quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyon
In physics, a dyon is a hypothetical particle in 4-dimensional theories with both electric and magnetic charges. A dyon with a zero electric charge is usually referred to as a magnetic monopole. Many grand unified theories predict the existence of both magnetic monopoles and dyons. Dyons were first proposed by Julian Schwinger in 1969 as a phenomenological alternative to quarks. He extended the Dirac quantization condition to the dyon and used the model to predict the existence of a particle with the properties of the J/ψ meson prior to its discovery in 1974. The allowed charges of dyons are restricted by the Dirac quantization condition. This states in particular that their magnetic charge must be integral, and that their electric charges must all be equal modulo 1. The Witten effect, demonstrated by Edward Witten in his 1979 paper, states that the electric charges of dyons must all be equal, modulo one, to the product of their magnetic charge and the theta angle of the th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because: * they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and * they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory. Relevant to dynamics, families of instantons permit that instantons, i.e. different critical points of the equation of motion, be rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Monopole
In particle physics, a magnetic monopole is a hypothetical particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from high-energy physics, particle theories, notably the grand unified theory, grand unified and superstring theory, superstring theories, which predict their existence. The known elementary particles that have electric charge are electric monopoles. Magnetism in bar magnets and electromagnets is not caused by magnetic monopoles, and indeed, there is no known experimental or observational evidence that magnetic monopoles exist. A magnetic monopole is not necessarily an elementary particle, and models for magnetic monopole production can include (but are not limited to) Spin (physics), spin-0 monopoles or spin-1 massive vector mesons. The term "magnetic monopole" only refers to the nature of the particle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphaleron
A sphaleron ( "slippery") is a static (time-independent) solution to the electroweak field equations of the Standard Model of particle physics, and is involved in certain hypothetical processes that violate baryon and lepton numbers. Such processes cannot be represented by perturbative methods such as Feynman diagrams, and are therefore called non-perturbative. Geometrically, a sphaleron is a saddle point of the electroweak potential (in infinite-dimensional field space). This saddle point rests at the top of a barrier between two different low-energy equilibria of a given system; the two equilibria are labeled with two different baryon numbers. One of the equilibria might consist of three baryons; the other, alternative, equilibrium for the same system might consist of three antileptons. In order to cross this barrier and change the baryon number, a system must either tunnel through the barrier (in which case the transition is an instanton-like process) or must for a reasonab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
