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QCD Vacuum
The QCD vacuum is the quantum vacuum state of quantum chromodynamics (QCD). It is an example of a ''non-perturbative'' vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter. Symmetries and symmetry breaking Symmetries of the QCD Lagrangian Like any relativistic quantum field theory, QCD enjoys Poincaré symmetry including the discrete symmetries CPT (each of which is realized). Apart from these space-time symmetries, it also has internal symmetries. Since QCD is an SU(3) gauge theory, it has local SU(3) gauge symmetry. Since it has many flavours of quarks, it has approximate flavour and chiral symmetry. This approximation is said to involve the chiral limit of QCD. Of these chiral symmetries, the baryon number symmetry is exact. Some of the broken symmetries include the axial U(1) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Vacuum State
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. However, the quantum vacuum is not a simple empty space, but instead contains fleeting electromagnetic waves and particles that pop into and out of the quantum field. The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s, it was reformulated by Feynman, Tomonaga, and Schwinger, who jointly received the Nobel prize for this work in 1965. For a historical discussion, see for example For the Nobel prize details and the Nobel lectures by these authors, see Today, the electromagnetic interactions and the weak interactions are unified (at very high energies only) in the theory of the electroweak interaction. The Standard Model is a generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SU(3)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on \mathbb^n. It is itself a subgroup of the general linear group, \operatorname(n) \subset \operatorname(n) \subset \operatorname(n, \mathbb ). The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics. The simplest case, , is the trivial group, having only a single element. The group is isomorphic to the group of quaternions of norm 1, and is thus diffeomorphic to the 3-sphere. Since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's ''energy spectrum'' or its set of ''energy eigenvalues'', is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory. The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by \hat, where the hat indicates that it is an operator. It can also be written as H or \check. Introduction The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Freedom
In quantum field theory, asymptotic freedom is a property of some gauge theory, gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases. (Alternatively, and perhaps contrarily, in applying an S-matrix, asymptotically free refers to free particles states in the distant past or the distant future.) Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the strong interaction between quarks and gluons, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing Perturbation theory (quantum mechanics), perturbative calculations. At low energies, the interaction becomes strong, leading to the color confinement, confinement of quarks and gluons within composite hadrons. The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the sam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Anomaly
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. In quantum field theory when we set Planck constant \hbar to zero we have only Feynman tree diagrams, which is a "classical" theory (equivalent to the Fredholm theory of a classical field theory). One-loop (''N''-loop) Feynman diagrams are proportional to \hbar (\hbar^N). If a current is conserved classically (\hbar=0) but develops a divergence at loop level in quantum field theory (\propto \hbar), we say there is an anomaly. A famous example is the axial current anomaly where massless fermions will have a classically conserved axial current, but which develops a nonzero divergence in the presence of gauge fields. A scale invariant theory, one in which there are no mass scales, will have a conserved Noether current called the "scale current." This is derived by performing scale transformations on the coordina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Symmetry
Conformal symmetry is a property of spacetime that ensures angles remain unchanged even when distances are altered. If you stretch, compress, or otherwise distort spacetime, the local angular relationships between lines or curves stay the same. This idea extends the familiar Poincaré group —which accounts for rotations, translations, and boosts—into the more comprehensive conformal group. Conformal symmetry encompasses special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 degrees of freedom: ten for the Poincaré group, four for special conformal transformations, and one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations. They called a generic expression of conformal symmetry a spherical wave transformation. General relativity in two spacetime dimensions also enjoys conformal symmetry. Generators The Lie algebra of the conformal grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poincaré Symmetry
Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science * Henriette Poincaré (1858–1943), wife of Prime Minister Raymond Poincaré * Lucien Poincaré (1862–1920), physicist, brother of Raymond and cousin of Henri * Raymond Poincaré (1860–1934), French Prime Minister or President ''inter alia'' from 1913 to 1920, cousin of Henri See also *List of things named after Henri Poincaré In physics and mathematics, a number of ideas are named after Henri Poincaré: * Euler–Poincaré characteristic * Hilbert–Poincaré series * Poincaré–Bendixson theorem * Poincaré–Birkhoff theorem * Poincaré–Birkhoff–Witt theorem, ... * {{DEFAULTSORT:Poincare French-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strong CP Problem
The strong CP problem is a question in particle physics, which brings up the following quandary: why does quantum chromodynamics (QCD) seem to preserve CP-symmetry? In particle physics, CP stands for the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). According to the current mathematical formulation of quantum chromodynamics, a violation of CP-symmetry in strong interactions could occur. However, no violation of the CP-symmetry has ever been seen in any experiment involving only the strong interaction. As there is no known reason in QCD for it to necessarily be conserved, this is a " fine tuning" problem known as the strong CP problem. The strong CP problem is sometimes regarded as an unsolved problem in physics, and has been referred to as "the most underrated puzzle in all of physics." There are several proposed solutions to solve the strong CP problem. The most well-known is Peccei–Quinn theory, involving new pseudoscalar particles ... [...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] |
Chiral Anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is analogous to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa. Such events are expected to be prohibited according to classical conservation laws, but it is known there must be ways they can be broken, because we have evidence of charge–parity non-conservation ("CP violation"). It is possible that other imbalances have been caused by breaking of a ''chiral law'' of this kind. Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly. Research into chiral symmetry breaking laws is a major endeavor in particle physics research at this time. Informal introduction The chiral anomaly originally referred to the anomalous decay rate of the neutral pion, as computed in the current algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baryon Number
In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as B = \frac(n_\text - n_), where is the number of quarks, and is the number of antiquarks. Baryons (three quarks) have B = +1, mesons (one quark, one antiquark) have B = 0, and antibaryons (three antiquarks) have B = −1. Exotic hadrons like pentaquarks (four quarks, one antiquark) and tetraquarks (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number. In the standard model B conservation is an accidental symmetry which means that it appears in the standard model but is often violated when going beyond it. Physics beyond the Standard Model theories that contain baryon number violation are, for example, Standard Model with extra dimensions, Supersymmetry, Grand Unified Theory and String theory. Baryon number vs. quark number Quarks carry not only electric charge, but also charges such as color charge and weak iso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
