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Encyclopedia > Quantum Chromodynamics
 Quantum physics $Delta x Delta p ge frac{hbar}{2}$ Quantum mechanics Introduction to... Mathematical formulation of... Fig. ... Werner Heisenberg and Erwin SchrÃ¶dinger, founders of QM. Quantum mechanics (QM, or quantum theory) is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ... Fundamental concepts Decoherence · Interference Uncertainty · Exclusion Transformation theory Ehrenfest theorem · Measurement In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... Experiments Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment EPR paradox · Popper's experiment Schrödinger's cat Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits, which produces fringes or wave-like interference patterns on a screen. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... In quantum mechanics, the Sternâ€“Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ... Poppers experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics. ... SchrÃ¶dingers Cat: If the nucleus in the bottom left decays, the Geiger counter on its right will sense it and trigger the release of the gas. ... Equations Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The Pauli equation is a SchrÃ¶dinger equation which handles spin. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the SchrÃ¶dinger equation. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Advanced theories Quantum field theory Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Quantum field theory (QFT) is the quantum theory of fields. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... This article or section does not adequately cite its references or sources. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... Interpretations Copenhagen · Quantum logic Hidden variables · Transactional Many-worlds · Ensemble Consistent histories · Relational Consciousness causes collapse Orchestrated objective reduction It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... In physics, a hidden variable theory is urged by a minority of physicists who argue that the statistical nature of quantum mechanics implies that quantum mechanics is incomplete; it is really applicable only to ensembles of particles; new physical phenomena beyond quantum mechanics are needed to explain an individual event. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... // Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, the state is the relation between the observer and the system. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Orch OR (â€œOrchestrated Objective Reductionâ€) is a theory of consciousness put forth in the mid-1990s by British theoretical physicist Sir Roger Penrose and American anesthesiologist Stuart Hameroff. ... Scientists Planck · Schrödinger Heisenberg · Bohr · Pauli Dirac · Bohm · Born de Broglie · von Neumann Einstein · Feynman Everett · Others Max Karl Ernst Ludwig Planck (April 23, 1858 â€“ October 4, 1947 in GÃ¶ttingen, Germany) was a German physicist. ... Erwin Rudolf Josef Alexander SchrÃ¶dinger (August 12, 1887 â€“ January 4, 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the SchrÃ¶dinger equation, for which he received the Nobel Prize in 1933. ... Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics, and acknowledged to be one of the most important physicists of the twentieth century. ... Niels (Henrik David) Bohr (October 7, 1885 â€“ November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... David Bohm. ... Max Born (December 11, 1882 in Breslau â€“ January 5, 1970 in GÃ¶ttingen) was a mathematician and physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... John von Neumann (Hungarian Margittai Neumann JÃ¡nos Lajos) (born December 28, 1903 in Budapest, Austria-Hungary; died February 8, 1957 in Washington D.C., United States) was a Hungarian-born American mathematician who made contributions to quantum physics, functional analysis, set theory, topology, economics, computer science, numerical analysis, hydrodynamics... Albert Einstein ( ) (March 14, 1879 â€“ April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... Richard Phillips Feynman (May 11, 1918 â€“ February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... Hugh Everett III (November 11, 1930 â€“ July 19, 1982) was an American physicist who first proposed the many-worlds interpretation(MWI) of quantum physics, which he called his relative state formulation. ... Below is a list of famous physicists. ... This box: view • talk • edit

Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). QCD is a quantum field theory of a special kind called a non-abelian gauge theory. It is an important part of the Standard Model of particle physics. A huge body of experimental evidence for QCD has been gathered over the years. The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... These are the six flavors of quarks and their most likely decay modes. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not adequately cite its references or sources. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: Ï€0, Ï€+ and Ï€âˆ’. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... Quantum field theory (QFT) is the quantum theory of fields. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ...

QCD enjoys two peculiar properties:

• Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly. That QCD predicts this behavior was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics.
• Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, it would take an infinite amount of energy to separate two quarks; they are forever bound into hadrons such as the proton and the neutron. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD.

In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i. ... The 1970s decade refers to the years from 1970 to 1979. ... Hugh David Politzer (born 31 August 1949) is an American theoretical physicist. ... Frank Wilczek (born May 15, 1951) is a Nobel prize winning American physicist. ... David Jonathan Gross (born February 19, 1941 in Washington, D.C.) is an American particle physicist and string theorist (although hes stated to the Brazilian newspaper Folha de SÃ£o Paulo, on 09/27/2006, that the second area is included in the first one). ... shelby was here 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Hannes AlfvÃ©n (1908â€“1995) accepting the Nobel Prize for his work on magnetohydrodynamics [1]. List of Nobel Prize laureates in Physics from 1901 to the present day. ... Colour confinement (often just confinement) is the physics phenomenon that color charged particles (such as quarks) cannot be isolated. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not adequately cite its references or sources. ... A free quark is a quark that is not bound to another quark (or, in general, not part of a color-neutral) group. ... It has been suggested that lattice field theory be merged into this article or section. ...

The word quark was coined by Murray Gell-Mann in its present sense, the word having been taken from the phrase "Three quarks for Muster Mark" in Finnegans Wake by James Joyce. These are the six flavors of quarks and their most likely decay modes. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... Finnegans Wake, published in 1939, is James Joyces final novel. ... James Augustine Aloysius Joyce (Irish SÃ©amus Seoighe; 2 February 1882 â€“ 13 January 1941) was an Irish expatriate writer, widely considered to be one of the most influential writers of the 20th century. ...

The three kinds of charge in QCD (as opposed to two in Quantum electrodynamics or QED) are usually referred to as "colour charge" by loose analogy to the three kinds of colour (red, green and blue) perceived by humans. Since the theory of electric charge is dubbed "electrodynamics", the Greek word "chroma" Χρώμα (meaning colour) is applied to the theory of colour charge, "chromodynamics". In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... Color is an important part of the visual arts. ... Color vision is a psychophysical phenomenon that exists only in our minds. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

## Lagrangian

The gauge invariant QCD Lagrangian is Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ...

where
$q ,$ is the quark field,
$gamma^mu ,$ are the Dirac matrices,
$G^a_mu ,$ are the 8 gauge fields, and
$T_a ,$ are the generators of the SU(3) group.

The term labeled $G^a_{mu nu} ,$ is similar to the Electromagnetic tensor, $F^{mu nu} ,$, found in Quantum electrodynamics. It is given by The Dirac equation is a relativistic quantum mechanical wave equation invented by Paul Dirac in 1928. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... This picture illustrates how the hours in a clock form a group. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ...

$G^a_{mu nu} = partial_mu G^a_{nu} - partial_nu G^a_mu - g f_{abc} G^b_mu G^c_nu ,$
where
$f_{abc} ,$ is known as the structure constant (see Gell-Mann matrices).

The Gell-Mann matrices, named after Murray Gell-Mann, are the infinitesimal generators of su(3). ...

## History

With the invention of bubble chambers and spark chambers in the 1950s, experimental particle physics discovered a large and ever-growing number of particles called hadrons. It seemed that such a large number of particles could not all be fundamental. First, the particles were classified by charge and isospin; then, in 1953, according to strangeness by Murray Gell-Mann and Kazuhiko Nishijima. To gain greater insight, the hadrons were sorted into groups having similar properties and masses using the eightfold way, invented in 1961 by Gell-Mann and Yuval Ne'eman. Gell-Mann and George Zweig went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavours of smaller particles inside the hadrons: the quarks. A bubble chamber A bubble chamber is a vessel filled with a superheated transparent liquid used to detect electrically charged particles moving through it. ... A spark-chamber detector is a particle detector, that is, a device used in particle physics for detecting electrically charged particles. ... This does not cite any references or sources. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... ... In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. ... Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ... 1953 (MCMLIII) was a common year starting on Thursday. ... In particle physics, strangeness, denoted as , is a property of particles, expressed as a quantum number for describing decay of particles in strong and electro-magnetic reactions, which occur in a short period of time. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... 1961 (MCMLXI) was a common year starting on Sunday (the link is to a full 1961 calendar). ... Yuval Neeman (May 14, 1925 â€“ April 26, 2006), was an Israeli physicist and politician. ... George Zweig was originally trained as a particle physicist under Richard Feynman and later turned his attention to neurobiology. ... Year 1963 (MCMLXIII) was a common year starting on Tuesday (link will display full calendar) of the Gregorian calendar. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... These are the six flavors of quarks and their most likely decay modes. ...

At this stage, one particle, the Δ++ remained mysterious; in the quark model, it is composed of three up quarks with parallel spins. However, since quarks are fermions, this combination is forbidden by the Pauli exclusion principle. In 1965, Moo-Young Han with Yoichiro Nambu and Oscar W. Greenberg independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called colour charge. Han and Nambu noted that quarks would interact via an octet of vector gauge bosons: the gluons. In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... 1965 (MCMLXV) was a common year starting on Friday (the link is to a full 1965 calendar). ... Dr. Moo-Young Han (1934- ) is a professor of physics at Duke University. ... Yoichiro Nambu (1921â€“) is a Japanese-born American physicist. ... Oscar Wallace Greenberg is a physicist and professor at University of Maryland, College Park. ... In mathematics, the special unitary group of degree n, denoted SU(n), is the group of nÃ—n unitary matrices with unit determinant. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ...

Since free quark searches consistently failed to turn up any evidence for the new particles, it was then believed that quarks were merely convenient mathematical constructs, not real particles. Richard Feynman argued that high energy experiments showed quarks to be real: he called them partons (since they were parts of hadrons). James Bjorken proposed that certain relations should then hold in deep inelastic scattering of electrons and protons, which were spectacularly verified in experiments at SLAC in 1969. Richard Phillips Feynman (May 11, 1918 â€“ February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... James Daniel BJ Bjorken is an American theoretical physicst. ... Deep Inelastic Scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons. ... e- redirects here. ... The Stanford Linear Accelerator Center (SLAC) is a U.S. national laboratory operated by Stanford University for the U.S. Department of Energy. ... For the Stargate SG-1 episode, see 1969 (Stargate SG-1). ...

Although the study of the strong interaction remained daunting, the discovery of asymptotic freedom by David Gross, David Politzer and Frank Wilczek allowed physicists to make precise predictions of the results of many high energy experiments using the techniques of perturbation theory. Evidence of gluons was discovered in three jet events at PETRA in 1979. These experiments became more and more precise, culminating in the verification of perturbative QCD at the level of a few percent at the LEP in CERN. In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i. ... David Jonathan Gross (born February 19, 1941 in Washington, D.C.) is an American particle physicist and string theorist (although hes stated to the Brazilian newspaper Folha de SÃ£o Paulo, on 09/27/2006, that the second area is included in the first one). ... Hugh David Politzer (born 31 August 1949) is an American theoretical physicist. ... Frank Wilczek (born May 15, 1951) is a Nobel prize winning American physicist. ... In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... The term three jet event, or Mercedes event, refers to particularly distinctive three-jet events found in particle detectors that constitute the most direct evidence currently available for the existence of gluons. ... Petra (from petra, rock in Greek; Arabic: Ø§Ù„Ø¨ØªØ±Ø§Ø¡, Al-ButrÄ) is an archaeological site in Jordan, lying in a basin among the mountains which form the eastern flank of Arabah (Wadi Araba), the large valley running from the Dead Sea to the Gulf of Aqaba. ... Also: 1979 by Smashing Pumpkins. ... Perturbative QCD is the study of the theory of Quantum chromodynamics in energy regimes where the strong coupling constant is small, allowing Perturbation theory to be applied. ... The Large Electron-Positron Collider (usually called LEP for short. ... CERN logo The Organisation europÃ©enne pour la recherche nuclÃ©aire (English: European Organization for Nuclear Research), commonly known as CERN, pronounced (or in French), is the worlds largest particle physics laboratory, situated just northwest of Geneva on the border between France and Switzerland. ...

The other side of asymptotic freedom is confinement. Since the force between colour charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. This aspect of the theory is verified within lattice QCD computations, but is not mathematically proven. One of the Millennium Prizes announced by the Clay Mathematics Institute requires a claimant to produce such a proof. Other aspects of non-perturbative QCD are the exploration of phases of quark matter, including the quark-gluon plasma. Colour confinement (often just confinement) is the physics phenomenon that color charged particles (such as quarks) cannot be isolated. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... It has been suggested that lattice field theory be merged into this article or section. ... The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts. ... In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. ... Quark matter or QCD matter refers to any of a number of phases of matter whose degrees of freedom include quarks and gluons. ... A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. ...

## The theory

Unsolved problems in physics: QCD in the non-perturbative regime:

Image File history File links No higher resolution available. ... This is a list of some of the unsolved problems in physics. ... In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ... Colour confinement (often just confinement) is the physics phenomenon that color charged particles (such as quarks) cannot be isolated. ... In physics, energy scale is a particular value of energy determined with the precision of one order (or a few orders) of magnitude. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... Quark matter or QCD matter refers to any of a number of phases of matter whose degrees of freedom include quarks and gluons. ... A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ...

### Some definitions

Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations. These can be Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

• local symmetries, that is the symmetry acts independently at each point in space-time. Each such symmetry is the basis of a gauge theory and requires the introduction of its own gauge bosons.
• global symmetries, which are symmetries whose operations must be simultaneously applied to all points of space-time.

QCD is a gauge theory of the SU(3) gauge group obtained by taking the colour charge to define a local symmetry. This article or section does not cite its references or sources. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... This article or section does not cite its references or sources. ... In mathematics, the special unitary group of degree n, denoted SU(n), is the group of nÃ—n unitary matrices with unit determinant. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ...

Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.

There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed. If the spin of a particle has a positive projection on its direction of motion then it is called left-handed; otherwise, it is right-handed. Chirality and handedness are not the same, but become approximately equivalent at high energies. A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... The transformation P is the orthogonal projection onto the line m. ...

• Chiral symmetries involve independent transformations of these two types of particle.
• Vector symmetries (also called diagonal symmetries) mean the same transformation is applied on the two chiralities.
• Axial symmetries are those in which one transformation is applied on left-handed particles and the inverse on the right-handed particles.

### The symmetry groups

The colour group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1) which is gauged to give QED: this is an abelian group. If one considers a version of QCD with Nf flavors of massless quarks, then there is a global (chiral) flavor symmetry group $SU_L(N_f)times SU_R(N_f)times U_B(1)times U_A(1)$. The chiral symmetry is spontaneously broken by the QCD vacuum to the vector (L+R) SUV(Nf) with the formation of a chiral condensate. The vector symmetry, UB(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry UA(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly. Gluon field configurations called instantons are closely related to this anomaly. Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In mathematics, an abelian group, also called a commutative group, is a group such that for all a and b in G. In other words, the order of elements in a product doesnt matter. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). ... This article or section should be merged with fermionic condensate In a theory with two chiral fields, &#968;1 and &#968;2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a fermion condensate (also called... In physics, an anomaly is a classical symmetry â€” a symmetry of the Lagrangian â€” that is broken in quantum field theories. ... This article or section is in need of attention from an expert on the subject. ...

#### Cautionary note

In many applications of QCD one can ignore the heavy flavors of quark (charm, bottom and top). In this case the effective flavor group is often SU(3), which should not be confused with the colour group. In QCD the colour group belongs to a local symmetry and hence is gauged. The flavor group is not gauged. The Eightfold way is based on the flavor group and ignores the local symmetry which gives QCD.

### The fields

Quarks are massive spin-1/2 fermions which carry a colour charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They also carry electric charge (either -1/3 or 2/3) and participate in weak interactions as part of weak isospin doublets. They carry global quantum numbers including the baryon number, which is 1/3 for each quark, hypercharge and one of the flavor quantum numbers. These are the six flavors of quarks and their most likely decay modes. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi-Dirac statistics. ... In mathematics, a fundamental representation is a representation of a mathematical structure, such as a group, that satisfies the following condition: All other irreducible representations of the group can be found in the tensor products of the fundamental representation with many copies of itself. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... The weak isospin in theoretical physics parallels the idea of the isospin under the strong interaction, but applied under the weak interaction. ... In particle physics, the baryon number is an approximate conserved quantum number. ... In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before... In particle physics, flavor is a property of a fermion that identifies it, a label that specifies the name of the particle. ...

Gluons are spin-1 bosons which also carry colour charges, since they lie in the adjoint representation 8 of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the singlet representation 1 of all these symmetry groups. In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... In mathematics, the adjoint representation (or adjoint action) of a Lie group G is the natural representation of G on its own Lie algebra. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... In theoretical physics, a singlet usually refers to a one-dimensional representation (e. ...

Every quark has its own antiquark. The charge of each antiquark is exactly the opposite of the corresponding quark.

### The dynamics

According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with QED, in which only the first kind of interaction occurs, since photons have no charge. We also have to consider diagrams involving Faddeev-Popov ghosts. Quantum field theory (QFT) is the quantum theory of fields. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... In physics, Faddeev-Popov ghost ci is a field that violates the spin-statistics relation. ...

## Methods

Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below.

### Perturbative QCD

This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date. In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ...

### Lattice QCD

Among non-perturbative approaches to QCD, the most well established one is lattice QCD. This approach uses a discrete set of space-time points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation which is then carried out on supercomputers. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means. It has been suggested that lattice field theory be merged into this article or section. ... A supercomputer is a device for turning compute-bound problems into I/O-bound problems. ...

### 1/N expansion

A well-known approximation scheme, the 1/N expansion, starts from the premise that the number of colours is infinite, and makes a series of corrections to account for the fact that it is not. Until now it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the AdS/CFT approach. In quantum field theory and statistical mechanics, the 1/N expansion is a particular perturbative analysis of quantum field theories with an SO(N) or SU(N) internal symmetry. ... In physics, the AdS/CFT correspondence is the equivalence between a string theory or supergravity defined on some sort of Anti de Sitter space and a conformal field theory defined on its boundary whose dimension is lower by one. ...

### Effective theories

For specific problems some theories may be written down which seem to give qualitatively correct results. In the best of cases, these may then be obtained as systematic expansions in some parameter of the QCD Lagrangian. Among the best such effective models one should now count chiral perturbation theory (which expands around light quark masses near zero), heavy quark effective theory (which expands around heavy quark mass near infinity), and soft-collinear effective theory (which expands around large ratios of energy scales). Other less accurate models are the Nambu-Jona-Lasinio model and the chiral model. Chiral perturbation theory is an effective field theory constructed on a lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics. ... In quantum field theory, soft-collinear effective theory (or SCET) is a theoretical framework for doing calculations in quantum chromodynamics (QCD) that involve interacting particles carrying widely different energies. ... In quantum field theory, the Nambu-Jona-Lasinio model is a theory of interacting Dirac fermions with chiral symmetry. ... In nuclear physics, the chiral model is a phenomenological model describing mesons in the chiral limit where the masses of the quarks goes to zero (without mentioning quarks at all). ...

## Experimental tests

The notion of quark flavours was prompted by the necessity of explaining the properties of hadrons during the development of the quark model. The notion of colour was necessitated by the puzzle of the Δ++. This has been dealt with in the section on the history of QCD. Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ...

The first evidence for quarks as real constitutent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC. The first evidence for gluons came in three jet events at PETRA. These are the six flavors of quarks and their most likely decay modes. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... Deep Inelastic Scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons. ... The Stanford Linear Accelerator Center (SLAC) is a U.S. national laboratory operated by Stanford University for the U.S. Department of Energy. ... The term three jet event, or Mercedes event, refers to particularly distinctive three-jet events found in particle detectors that constitute the most direct evidence currently available for the existence of gluons. ... Petra (from petra, rock in Greek; Arabic: Ø§Ù„Ø¨ØªØ±Ø§Ø¡, Al-ButrÄ) is an archaeological site in Jordan, lying in a basin among the mountains which form the eastern flank of Arabah (Wadi Araba), the large valley running from the Dead Sea to the Gulf of Aqaba. ...

Good quantitative tests of perturbative QCD are

Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through lattice computations of heavy-quarkonium spectra. There is a recent claim about the mass of the heavy meson Bc [1]. Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and form factors of hadrons and their weak matrix elements are promising candidates for future quantitative tests. The whole subject of quark matter and the quark-gluon plasma is a non-perturbative test bed for QCD which still remains to be properly exploited. In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... Deep Inelastic Scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons. ... A vector boson is a boson with spin equal to one. ... a Drell-Yan process takes place when a quark and an anti-quark of a nucleon annihilate and create new particles. ... The Large Electron-Positron Collider (usually called LEP for short. ... It has been suggested that lattice field theory be merged into this article or section. ... Form factor refers to the linear dimensions and configuration of a device as distinguished from other measures of size (for example Gigabytes; a measure of storage size): in computing, form factor is used to describe the size and format of PC motherboards (see AT, ATX, BTX), but also of hard... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ... A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. ...

The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... This is a detailed description of the standard model (SM) of particle physics. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... These are the six flavors of quarks and their most likely decay modes. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... Colour confinement (often just confinement) is the physics phenomenon that color charged particles (such as quarks) cannot be isolated. ... Quark matter or QCD matter refers to any of a number of phases of matter whose degrees of freedom include quarks and gluons. ... A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... See gauge theory for the classical prelimanaries. ... Possible alternative meanings of BRST are: BRST formalism Big Red Switch Time (or Big Red Switch Treatment): computer jargon for switching your computer off, when all other options for a more elegant shutdown have been exhausted. ... In physics, Faddeev-Popov ghost ci is a field that violates the spin-statistics relation. ... Quantum field theory (QFT) is the quantum theory of fields. ... It has been suggested that lattice field theory be merged into this article or section. ... In quantum field theory and statistical mechanics, the 1/N expansion is a particular perturbative analysis of quantum field theories with an SO(N) or SU(N) internal symmetry. ... Perturbative QCD is the study of the theory of Quantum chromodynamics in energy regimes where the strong coupling constant is small, allowing Perturbation theory to be applied. ... In nuclear physics, the chiral model is a phenomenological model describing mesons in the chiral limit where the masses of the quarks goes to zero (without mentioning quarks at all). ... In quantum field theory, the Nambu-Jona-Lasinio model is a theory of interacting Dirac fermions with chiral symmetry. ... Deep Inelastic Scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons. ... A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. ...

• Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2.
• Particle data group
• The millennium prize for proving confinement

Results from FactBites:

 Quantum chromodynamics - Wikipedia, the free encyclopedia (2007 words) Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). The three kinds of charge in QCD (as opposed to one in Quantum electrodynamics or QED) are usually referred to as "color charge" by loose analogy to the three kinds of color (red, green and blue) perceived by humans. They carry global quantum numbers including the baryon number, which is 1/3 for each quark, hypercharge and one of the flavor quantum numbers.
 AllRefer.com - quantum chromodynamics (Physics) - Encyclopedia (349 words) quantum chromodynamics (QCD), quantum field theory that describes the properties of the strong interactions between quarks and between protons and neutrons in the framework of quantum theory. QCD is nearly identical in mathematical structure to quantum electrodynamics (QED) and to the unified theory of weak and electromagnetic interactions advanced by American physicist Steven Weinberg and Pakistani physicist Abdus Salam. See F. Yndurain, Quantum Chromodynamics: An Introduction to the Theory of Quarks and Gluons (1983); G. Altarelli, The Development of Perturbative QCD (1994); W. Greiner and A. Schafer, Quantum Chromodynamics (1994).
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