Color charge

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In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics (QCD). Color charge has analogies with the notion of electric charge of particles, for example it is a conserved charge, but because of the mathematical complications of QCD, there are many technical differences.
The "color charge" of quarks and gluons is completely unrelated to visual perception of color,^{1} because it is a property that has almost no manifestation at distances above the size of an atomic nucleus. The term color was chosen because the charge responsible for the strong force between particles can be analogized to the three primary colors of light: red, green, and blue.^{2} Another color scheme is "red, yellow, and blue",^{3} for analogy to paint. The analogy is only in the name, and the way colors mix, nothing more.
All three colors mixed together, or any one of these colors and its complement (or negative), is "colorless" or "white". This is how the color charge on particles behaves. A combination of three particles, one with red charge, another with green charge, and another blue charge, has a net color charge of zero ("colorless"), and this combination does not interact with other color charges. Particles have corresponding antiparticles. A particle with red, green, or blue charge has a corresponding antiparticle in which the color charge must be the color complement of red, green, and blue, respectively, for the color charge to be conserved in particleantiparticle creation and annihilation. Particle physicists call these antired, antigreen, and antiblue. In all, color charge has three values, and three negatives.
All free particles have a color charge of zero. Baryons are composed of three quarks, and have a net color charge of zero but the individual quarks can have red, green, or blue charges, or negatives. Mesons are made from a quark and antiquark, and again have a net color charge of zero, but the quark can be any color, and the antiquark will have the negative of that color.
By comparison, the electromagnetic charge has only one kind of value. Positive and negative electrical charges are the same kind of charge, as they only differ by the sign. A particle with positive charge has a corresponding antiparticle with a negative charge.
Historically, 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 quantum states without violating the Pauli exclusion principle. The theory of quantum chromodynamics has been under development since the 1970s and constitutes an important component of the Standard Model of particle physics.^{citation needed}
Contents
Red, green, and blue
In QCD, a quark's color can take one of three values or charges, red, green, and blue. An antiquark can take one of three anticolors, called antired, antigreen, and antiblue (represented as cyan, magenta and yellow, respectively). Gluons are mixtures of two colors, such as red and antigreen, which constitutes their color charge. QCD considers eight gluons of the possible nine color–anticolor combinations to be unique; see eight gluon colors for an explanation.
The following illustrates the coupling constants for colorcharged particles:
Field lines from color charges
Analogous to an electric field and electric charges, the strong force acting between color charges can be depicted using field lines. However, the color field lines do not arc outwards from one charge to another as much, because they are pulled together tightly by gluons (within 1 fm).^{4} This effect confines quarks within hadrons.
Coupling constant and charge
In a quantum field theory, a coupling constant and a charge are different but related notions. The coupling constant sets the magnitude of the force of interaction; for example, in quantum electrodynamics, the finestructure constant is a coupling constant. The charge in a gauge theory has to do with the way a particle transforms under the gauge symmetry; i.e., 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 (using tensor index notation):

 , and
where 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 nonabelian theory, the representations, and hence the color charges, are more complicated. They are dealt with in the next section.
Quark and gluon fields and color charges
In QCD the gauge group is the nonabelian group SU(3). The running coupling is usually denoted by α_{s}. Each flavor 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

 and
The gluon contains an octet of fields (see gluon field), and belongs to the adjoint representation (8), and can be written using the GellMann matrices as
(there is an implied summation over a = 1, 2, ... 8). 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 have a color charge of red, green or blue and antiquarks have a color charge of antired, antigreen or antiblue. Gluons have a combination of two color charges (one of red, green or blue and one of antired, antigreen and antiblue) in a superposition of states which are given by the GellMann matrices. All other particles have zero color charge. Mathematically speaking, the color charge of a particle is the value of a certain quadratic Casimir operator in the representation of the particle.
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 → U ψ, where U is a 3 × 3 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 bookkeeping 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 colorline representation. The meaning is the following. Let ψ_{i} represent the ith component of a quark field (loosely called the ith color). The color of a gluon is similarly given by A which corresponds to the particular GellMann 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 q_{i} → g_{i j} + q_{j}. The colorline representation tracks these indices. Color charge conservation means that the ends of these colorlines must be either in the initial or final state, equivalently, that no lines break in the middle of a diagram.
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 colorline representation. The colorline 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 nonabelian 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.
See also
Look up color charge in Wiktionary, the free dictionary. 
References
 ^ Feynman, Richard (1985), QED: The Strange Theory of Light and Matter, Princeton University Press, p. 136, ISBN 0691083886, "The idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of 'color,' which has nothing to do with color in the normal sense."
 ^ Close (2007)
 ^ R. Penrose (2005). The Road to Reality. Vintage books. p. 648. ISBN 9780099440680.
 ^ R. Resnick, R. Eisberg (1985), Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd ed.), John Wiley & Sons, p. 684, ISBN 9780471873730
 ^ Parker, C.B. (1994), McGraw Hill Encyclopaedia of Physics (2nd ed.), Mc Graw Hill, ISBN 0070514003
 ^ M. Mansfield, C. O’Sullivan (2011), Understanding Physics (4th ed.), John Wiley & Sons, ISBN 9780470746370
Further reading
 Georgi, Howard (1999), Lie algebras in particle physics, Perseus Books Group, ISBN 0738202339.
 Griffiths, David J. (1987), Introduction to Elementary Particles, New York: John Wiley & Sons, ISBN 0471603864.
 Christman, J. Richard (2001), "Colour and Charm", Project PHYSNET document MISN0283.
 Hawking, Stephen (1998), A Brief History of Time, Bantam Dell Publishing Group, ISBN 9780553109535.
 Close, Frank (2007), The New Cosmic Onion, Taylor & Francis, ISBN 1584887982.
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