Limits of Yang-Mills {alpha}-connections

In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps, we identify Yang-Mills connections obtained by approximations with respect to the Yang-Mills {alpha}-energy. More specifically, we show that for the SU(2) Hopf fibration over the four sphere, for sufficiently small {alpha} values the SO(4) invariant ADHM instanton is the unique {alpha}-critical point which has Yang-Mills {alpha}-energy lower than a specific threshold.