THE NUCLEUS is a collection of protons and neutrons (nucleons) held together by the strong nuclear force. The nucleon is, in turn, a composite object consisting of quarks bound by the same strong force. Moreover, free quarks and the strong "glue" that holds them together --- the gluon --- are not observed in Nature. All these are described by a theory called Quantum Chromodyamics (QCD) in which the quarks and gluons (partons) are endowed with colour charges --- a generalisation of the electric charge in electromagnetism. The interplay between different colours dictates the dynamics of their bearers, including the fascinating phenomenon of "asymptotic freedom" which is ultimately related to the confinement of quarks within nuclei.
Confinement is a consequence of the coupling strength between partons growing at large distances. This means that the traditional techniques of perturbation theory, which is used to predict properties of electromagnetic interactions, cannot be generally used in QCD. A non-perturbative approach is required. Lattice QCD allows us to extract some information about the non-perturbative aspects of QCD and to predict characteristics of the strong nuclear force. The construction of Lattice QCD may be explained in a number of steps.
Step 1 Transform continuous 4D space-time into a lattice. This discretisation consists of lattice sites (or vertices) which are joined by links. The simplest lattice geometry is hypercubic, but more elaborate constructions may be used. The hypercubic construction is much like the scaffolding at a construction site, except that it is four-dimensional. The reason for doing this is to give the Feynman Path Integral for QCD a definition. It will be through this path integral that all the non-perturbative physics will be extracted.
Step 2 At each lattice site, quarks and antiquarks are allowed to exist. The quarks will have different flavours (up, down, strange, charm, top and bottom) and colours (red, blue and green).
Step 3 On the links of the lattice, gluons are allowed to exist. The gluons mediate the interactions between the quarks on the lattice sites, much like the photons of electromagnetism which mediate the interactions between electrically charged particles. However, unlike the photon, a gluon carries colour charges and can directly interact with other gluons.
Step 4 The Action is a functional from which all the physics of QCD can be derived. Because space-time is now discrete, a discrete Action must be defined. There is no unique way of doing this. However a few considerations will help us decide: The discrete Action should reduce to the original (continuum) Action when the lattice spacing is taken to zero (continuum limit). The discrete Action should also observe the colour symmetry, even for non-zero lattice spacing. This is important, as it is this symmetry which characterises the strong nuclear force.
Step 5 By summing over all possible quark and gluon wave-fucntions and taking the continuum limit, physically measureable quantities associated with the strong nuclear force may be extracted. As an example, the ratio of the mass of the proton to the mass of the rho meson has been calculated in lattice QCD to be 1.254 +/- 0.045. This compares well with the experimental value of 1.22.