Gauge singularities in the SU(2) vacuum on the lattice Original Research Article

I summarize and extend the qualitative results, obtained previously by inspection of SU(2) lattice gauge field configurations. These configurations were generated by the Wilson action, then transformed to a Landau gauge and smoothed by Fourier filtering. This leads to sharp peaks in field strengths and related quantities, the characteristics of which are very well separated from a background. These spikes are caused by gauge singularities. Their density is determined as image, with very good scaling properties as a function of the bare coupling constant. The net number of spikes within a configuration vanishes when approaching the deconfinement region. Furthermore, the Landau-gauging procedure becomes unique, if the probability to find a spike is much smaller than unity. The relation of the spikes to the instantons obtained by cooling is investigated. Finally, a correlation between the presence of spikes and the infrared behaviour of the gluon propagator is demonstrated.