Aharonov–Bohm effect in lattice Abelian Higgs theory

We study a field-theoretical analogue of the Aharonov–Bohm effect in two-, three- and four-dimensional Abelian Higgs models; the corresponding topological interaction is proportional to the linking number of the Abrikosov vortex and the particle world trajectories. We show that the Aharonov–Bohm effect gives rise to a nontrivial interaction of charged test particles. The numerical calculations in the three-dimensional model confirm this fact.