Quantum chromodynamics theory (QCD) describes the interactions between quarks in high energy physics. QCD was constructed on analogy to quantum electrodynamics (QED), the quantum theory of the electromagnetic force. In QED, the electromagnetic interactions of charged particles are described through the emission and subsequent absorption of massless photons. by analogy with QED, quantum chromodynamics has been built upon the concept that quarks interact via the strong force because they carry a form of "strong charge," which has been given the name of color; other particles, such as the electron, which do not carry the color charge, do not interact in this way.

There are five types of quarks knowed by now (referred to as ``flavors''): up, down, strange, charm, and bottom. Another one (top)is expected to show up soon. In addition to having a ``flavor'', quarks can carry one of three (red,green and blue) possible charges known as ``color'' (the color term, is just to distinguish ! a property, and do not means the color as we know it). This is why the theory is called quantum chromodynamics. The strong color force is mediated by particles called gluons, just as photons mediate the electromagnetic force. Unlike photons, though, gluons themselves carry a color charge and, therefore, interact with one another. This makes QCD a nonlinear theory, which is impossible to solve analytically. The solutions have to be done by computers. QCD is an example of a ``gauge theory''. These are quantum field theories that have a local symmetry described by a symmetry (or gauge) group. Gauge theories are ubiquitous in elementary particle physics: The electromagnetic interaction between electrons and photons is described by quantum electrodynamics (QED) based on the gauge group U(1); the strong force between quarks and gluons is believed to be explained by QCD based on the group SU(3); and there is a unified description of the weak and electromagnetic interactions in terms of the gauge group . The strength of these interactions is measured by a coupling constant. This coupling constant is small for QED, so very precise analytical calculations can be performed using perturbation theory, and these agree extremely well with experiment. However, for QCD, the coupling appears to increase with distance (which is why we never see an isolated quark, since they are always bound together by the strength of the coupling between! them). Perturbative calculations are therefore only possible at short distances (or large energies).

In order to solve QCD at longer distances, Wilson introduced lattice gauge theory, in which the space-time continuum is discretized and a discrete version of the gauge theory is derived which keeps the gauge symmetry intact. This discretization onto a lattice, which is typically hypercubic (four dimentions), gives a nonperturbative approximation to the theory that is successively improvable by increasing the lattice size and decreasing the lattice spacing, and provides a simple and natural way of regulating the divergences which plague perturbative approximations. This also helps to make the gauge theory amenable to numerical simulation by computer.