Cooling for instantons and the wrath of Nahm

The dynamics of instantons and anti-instantons in lattice QCD can be studied by analysing the action and topological charge of configurations as they approach a self-dual or anti-self-dual state, i.e. a state in which S/S-0 = \Q\. We use cooling to reveal the semi-classical structure of the configurations we study. Improved actions which eliminate discretisation errors up to and including O(a(4)) are used to stabilise instantons as we cool for several thousand sweeps. An analogously improved lattice version of the. continuum field-strength tensor is used to construct a topological charge free from 0(a 4) discretisation errors, Values of the action and topological charge obtained with these improved operators approach mutually-consistent integer values to within a few parts in 104 after several hundred cooling sweeps. Analysis of configurations with \Q\ approximate to 1 and \Q\ approximate to 2 supports the hypothesis that a self-dual \Q\ = 1 configuration cannot exist on the 4-torus.