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Encyclopedia > Color charge

In particle physics, color charge is a property of quarks and gluons which are related to their strong interactions in the context of quantum chromodynamics (QCD). This has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD, there are many technical differences. The "color" of quarks and gluons have nothing to do with the visual perception of color, but is a whimsical name for a property which has almost no manifestation at distances above the size of an atomic nucleus. Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... The Gluon is the basic unit of Elmers Glue. ... 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. ... Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... A stylized representation of a lithium atom. ...


Shortly after the existence of quarks was first proposed in 1964, Oscar W. Greenberg introduced the notion of color charge to explain how quarks could coexist inside some hadrons in otherwise identical states and still satisfy the Pauli exclusion principle. The concept turned out to be useful. Quantum chromodynamics has been under development since the 1970s and constitutes an important ingredient in the standard model of particle physics. Oscar Wallace Greenberg is a physicist and professor at University of Maryland, College Park. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... 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. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ...

Contents


Red, blue and green

One can say that a quark's color can take three values: "red", "green", or "blue"; and that an antiquark can take on three "anticolors", sometimes called "antired", "antigreen" and "antiblue" (occassionally represented as cyan, magenta and yellow). In the same vein it can be said that gluons are mixtures of two colours: for example red-antigreen, and this constitutes their color charge. Also it is further stated that there are eight gluons, leaving one to figure out where the ninth one went. In this language, the answer is that one particular combination: the (red-antired)+(blue-antiblue)+(green-antigreen) is actually colourless and hence does not need to be considered any more. This is about as far as one can push this language. Further elaboration requires a little bit of background which the next sections build and use. One should read them along with the companion article on coupling constants. In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ...


Coupling constant and charge

In a quantum field theory the notion of a coupling constant and a charge are different but related. The coupling constant sets the magnitude of the force of interaction; for example, in quantum electrodynamics, the fine structure constant is a coupling constant. The charge in a gauge theory has to do with the way a particle transforms under the gauge symmetry, ie, its representation under the gauge group. For example, the electron has charge -1 and the positron has charge +1, implying that the gauge transformation has opposite effects on them in some sense. Specifically, if a local gauge transformation φ(x) is applied in electrodynamics, then one finds Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... This article may be too technical for most readers to understand. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... 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, a group representation is a way of viewing a group in some more concrete way. ... The term group can refer to several concepts: Look up Group on Wiktionary, the free dictionary In music, a group is another term for band or other musical ensemble. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

,     and 

where Aμ is the photon field, and ψ is the electron field with Q=-1 (a bar over ψ denotes its antiparticle— the positron). Since QCD is a non-Abelian theory, the representations, and hence the color charges, are more complicated. They are dealt with in the next section. For the Science Fiction weapon, as seen in Star Trek, see Photon torpedo. ... In mathematics, an abelian group is a commutative group, i. ...


Quark and gluon fields and color charges

In QCD the gauge group is the non-Abelian group SU(3). The running coupling is usually denoted by αs. Each flavour of quark belongs to the fundamental representation (3) and contains a triplet of fields together denoted by ψ. The antiquark field belongs to the complex conjugate representation (3*) and also contains a triplet of fields. We can write 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 physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... 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. ... In mathematics, a group representation is a way of viewing a group in some more concrete way. ...

 and 

The gluon contains an octet of fields, belongs to the adjoint representation (8), and can be written using the Gell-Mann matrices as The adjoint representation of a Lie group G is the linearized version of the action of G on itself by conjugation. ... The Gell-Mann matrices, named after Murray Gell-Mann, are the infinitesimal generators of su(3). ...

All other particles belong to the trivial representation (1) of color SU(3). The color charge of each of these fields is fully specified by the representations. Quarks and antiquarks have color charge 4/3, whereas gluons have color charge 8. All other particles have zero colour charge. Mathematically speaking, the color charge of a particle is the value of a certain quadratic Casimir operator in the representation of the particle. A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... In mathematics, in particular group representation theory, a group representation of the group G is called a trivial representation if (i) it is defined on a one-dimensional vector space V over a field K and (ii) all elements g of G act on V as the identity mapping. ... 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 mathematics, a Casimir invariant of a Lie algebra is a member of the center of the universal enveloping algebra of the Lie algebra. ...


In the simple language introduced previously, the three indices "1", "2" and "3" in the quark triplet above are usually identified with the three colors. The colorful language misses the following point. A gauge transformation in color SU(3) can be written as ψ → Uψ, where U is a 3X3 matrix which belongs to the group SU(3). Thus, after gauge transformation, the new colors are linear combinations of the old colors. In short, the simplified language introduced before is not gauge invariant.

Color charge is conserved, but the book-keeping involved in this is more complicated than just adding up the charges, as is done in quantum electrodynamics. One simple way of doing this is to look at the interaction vertex in QCD and replace it by a colour line representation. The meaning is the following. Let ψi represent the i-th component of a quark field (loosely called the i-th color). The color of a gluon is similarly given by a which corresponds to the particular Gell-Mann matrix it is associated with. This matrix has indices i and j. These are the color labels on the gluon. At the interaction vertex one has qi→gij+qj. The color-line representation tracks these indices. Color charge conservation means that the ends of these color-lines must be either in the initial or final state , equivalently, that no lines break in the middle of a diagram. QCD vertex and color line representation File links The following pages link to this file: Color charge ...

Since gluons carry color charge, two gluons can also interact. A typical interaction vertex (called the three gluon vertex) for gluons involves g+g→g. This is shown here, along with its color line representation. The color-line diagrams can be restated in terms of conservation laws of color, however, as noted before, this is not a gauge invariant language. Note that in a typical non-Abelian gauge theory the gauge boson carries the charge of the theory, and hence has interactions of this kind; for example, the W boson in the electroweak theory. In the electroweak theory, the W also carries electric charge, and hence interacts with a photon. Image File history File links Three gluon vertex asnd color line representation File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ...


See also

Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... 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. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... The Gluon is the basic unit of Elmers Glue. ...

References

  • Howard Georgi, Lie algebras in particle physics, (1999) Perseus Books Group, ISBN 0738202339.
  • David J. Griffiths, Introduction to Elementary Particles, (1987) John Wiley & Sons, New York ISBN 0471603864
  • J. Richard Christman, Color and Charm, (2001) Project PHYSNET document MISN-0-283.

  Results from FactBites:
 
Color charge - Wikipedia, the free encyclopedia (966 words)
Quarks and antiquarks have color charge 4/3, whereas gluons have color charge 8.
Mathematically speaking, the color charge of a particle is the value of a certain quadratic Casimir operator in the representation of the particle.
Color charge conservation means that the ends of these color-lines must be either in the initial or final state, equivalently, that no lines break in the middle of a diagram.
Color charge - definition of Color charge in Encyclopedia (779 words)
Color was originally introduced as a means of reconciling simple quark models of baryons with the Pauli exclusion principle.
The role of color charge in QCD is analogous to that of electric charge in quantum electrodynamics (QED), the quantum theory of electricity and magnetism.
Since particles of different color are very strongly attracted and particles of like color repel very strongly, it follows that observable particles (those that survive for an appreciable length of time, such as protons and neutrons) are color-neutral (more precisely, quarks seem to exhibit confinement).
  More results at FactBites »

 
 

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