QCD calculations on the lattice

A basic explanation is given of the possibilities and limitations of lattice calculations. In the lattice formulation of QCD, Euclidean space-time is replaced by the vertices of a normally hypercubical lattice, and the dynamic variables are quark fields defined over the sites of the lattice. Gluonic fields are finite elements of the color group. The action contains a pure gauge part and a matter part. Three categories of numerical lattice calculations are described, divided according to the computational resources required. The first category involves calculations which make use of the quenched approximation and where the observables to be evaluated involve no quarks or involve quarks as static spectators only. The second consists of calculations performed within the quenched approximation, but where the observables involve propagating quarks. The most complex calculations fall in the final category, those where one tries to incorporate the dynamic effects from creation and annihilation of virtual quark pairs. 8 refs