Analytical and Numerical Study of the Aharonov--Bohm Effect in 3D and 4D Abelian Higgs Model

We discuss the Aharonov–Bohm effect in three and four dimensional non–compact lattice Abelian Higgs model. We show analytically that this effect leads to the long–range Coulomb interaction of the charged particles, which is confining in three dimensions. The Aharonov–Bohm effect is found in numerical calculations in 3D Abelian Higgs model.