We consider the gauge potential A and argue that the minimum value of the volume integral of A2 (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and noncompact "photodynamics" shows a jump in this quantity at the phase transition, supporting this idea.

We discuss phenomenology of the vacuum condensate (A a µ ) 2 min in pure gauge theories, where A a µ is the gauge potential. Both Abelian and non-Abelian cases are considered. In case of the compact U (1) the non-perturbative part of the condensate (A a µ ) 2 min is saturated by monopoles. In the non-Abelian case, a two-component picture for the condensate is presented according to which finite values of order Λ 2 QCD are associated both with large and short distances. We obtain a lower bound on the (A a µ ) 2 min by considering its change at the phase transition. Numerically, it produces an estimate similar to other measurements. Possible physical manifestations of the condensate are discussed.

Propagators of the diagonal and the off-diagonal gluons are studied numerically in the Maximal Abelian gauge of SU(2) lattice gauge theory. It is found that in the infrared region the propagator of the diagonal gluon is strongly enhanced in comparison with the off-diagonal one. The enhancement factor is about 50 at our smallest momentum 325 MeV. We have also applied various fits to the propagator formfactors.