Hidden singularities in non-abelian gauge fields

It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the case, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain Aμ (associated with the given regularization) represents the vacuum when Fμv is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A sub(approximately)=i σ sub(approximately)Λ r sub(approximately)/r2. For this example, it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point. (Author)