REMARKS ON ABELIAN DOMINANCE

We use a renormalization group based smoothing to address two question s related to Abelian dominance. Smoothing drastically reduces short di stance fluctuations but it preserves the long distance physical proper ties of the SU(2) configurations. This enables us to extract the Abeli an heavy-quark potential from timelike Wilson loops on Polyakov gauge- projected configurations. We obtain a very small string tension which is inconsistent with the string tension extracted from Polyakov loop c orrelators. This shows that the Polyakov gauge-projected Abelian confi gurations do not have a consistent physical meaning. We also apply the smoothing on SU(2) configurations to test how sensitive Abelian domin ance in the maximal Abelian gauge is to the short distance fluctuation s. We find that on smoothed SU(2) configurations the Abelian string te nsion was about 30% smaller than the SU(2) string tension which was un affected by smoothing. This suggests that the approximate Abelian domi nance found with the Wilson action is probably an accident and it has no fundamental physical relevance. [S0556-2821(97)04623-7].