Cooling, Physical Scales and Topology

We develop a cooling method controlled by a physical cooling radius that defines a scale below which fluctuations are smoothed out while leaving physics unchanged at all larger scales. We apply this method to study topological properties of lattice gauge theories, in particular the behaviour of instantons, dislocations and instanton anti-instanton pairs. Monte Carlo results for the SU(2) topology are presented. We find that the method provides a means to prevent instanton anti-instanton annihilation under cooling. While the instanton sizes are largely independent from the smoothing scale, the density and pair separations are determined by the particular choice made for this quantity. We discuss the questions this raises for the “physicality” of these concepts.