Quantum chromodynamics

QCD exhibits three salient properties: Physicist Murray Gell-Mann coined the word quark in its present sense.

On June 27, 1978, Gell-Mann wrote a private letter to the editor of the Oxford English Dictionary, in which he related that he had been influenced by Joyce's words: "The allusion to three quarks seemed perfect."

First, the particles were classified by charge and isospin by Eugene Wigner and Werner Heisenberg; then, in 1953–56,[8][9][10] according to strangeness by Murray Gell-Mann and Kazuhiko Nishijima (see Gell-Mann–Nishijima formula).

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[11] and Yuval Ne'eman.

Gell-Mann and George Zweig, correcting an earlier approach of Shoichi Sakata, went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavors of smaller particles inside the hadrons: the quarks.

In order to realize an antisymmetric orbital S-state, it is necessary for the quark to have an additional quantum number.Boris Struminsky was a PhD student of Nikolay Bogolyubov.

[15] In the beginning of 1965, Nikolay Bogolyubov, Boris Struminsky and Albert Tavkhelidze wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom.

In 1964–65, Greenberg[19] and Han–Nambu[20] independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called color charge.

The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions could probably not be fully described by quantum field theory.

Richard Feynman argued that high energy experiments showed quarks are real particles: he called them partons (since they were parts of hadrons).

James Bjorken proposed that pointlike partons would imply certain relations in deep inelastic scattering of electrons and protons, which were verified in experiments at SLAC in 1969.

As mentioned, asymptotic freedom means that at large energy – this corresponds also to short distances – there is practically no interaction between the particles.

However, as already mentioned in the original paper of Franz Wegner,[23] a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the original model, e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!)

dual model, namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances.

are the gluon fields, dynamical functions of spacetime, in the adjoint representation of the SU(3) gauge group, indexed by a, b and c running from

), which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large distances, similar to the entropic elasticity of a rubber band (see below).

This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies.

This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation that is then carried out on supercomputers like the QCDOC, which was constructed for precisely this purpose.

While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between quarks and antiquarks in a meson.

However, the numerical sign problem makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).

A well-known approximation scheme, the 1⁄N expansion, starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not.

The first evidence for quarks as real constituent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC.

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 that still remains to be properly exploited.

[citation needed] One qualitative prediction of QCD is that there exist composite particles made solely of gluons called glueballs that have not yet been definitively observed experimentally.

But, as of 2013, scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them.

In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the entropy plays an important role (see below).

For positive J0 the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "frustration" at all.

Energetically, perfect absence of frustration should be non-favorable and atypical for a spin glass, which means that one should add the loop product to the Hamiltonian, by some kind of term representing a "punishment".

The non-abelian character of the SU(3) corresponds thereby to the non-trivial "chemical links", which glue different loop segments together, and "asymptotic freedom" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for