Topological quantum dynamics of charged bosons

Using the Nielson–Olesen Lagrangian, we write down the system of coupled field equations and discuss some particular solutions. For a constant magnetic field, we work out the Klein–Gordon equation and derive a non-trivial current density. As we focus on the term in the vector-potential expressing pure topological effects, we derive the solution of the Klein–Gordon equation and the corresponding current density, in terms of the Aharonov–Bohm flux. It turns out that a radially non-homogeneous azimuthal current can be induced by a potentially-based electric field, of pure quantum origin.