The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 204 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 ≤ β ≤ 6.7, although we are not able to quantify the discrepencies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15 % at β = 6.1, while at β = 6.3 the change was less than 1 %. The potential between three charges is studied and yields a string tension of .18 GeV2, consistent with mesonic calculations and relativised potential models. Contributions to the potential from low-energy string vibrations appear small in the range x ≾ .5 fm. We perform energy density measurements in the colour fields surrounding both mesons and baryons, which provide strong evidence in favour of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise.
Several algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by colour sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at-large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable.
We discuss methods for the simulation of full QCD, including the effects of dynamical fermions. The Langevin approach is analysed in detail, and the systematic error associated with the discretisation of the equations of motion is derived. We propose a mixed Langevin/Metropolis algorithm and explore its properties on a small lattice. Finally, the method is tested on the finite temperature deconfinement transition and applied to the mesonic potential. It is found that shielding effects lead to deconfinement at β = 6.1 on a lattice of size 122 x 162.
