Instanton interactions at the one-loop level

We discuss the interactions between widely separated instantons (but not instantons and anti-instantons) due to the one-loop fluctuations in a non-Abelian gauge theory. A slightly generalized version of the recent calculation of Brown and Creamer for the one-loop determinant about an exact self-dual solution is used as a starting point. An apparently dangerous $\frac{1}{r^2}$ interaction is found to disappear with the proper parametrization of the exact solution. As a by-product of our procedure, we develop a more precise understanding of the relation between exact solutions of topological charge $k$ and the superposition of $k$ instantons. In particular, the meaning of the parameters of the Jackiw-Nohl-Rebbi $k=2\mathrm{}$ solution is understood in these terms.