The role of spatial topology in a toy model of classical electrodynamics in (1+1)(1+1) dimensions

We discuss the role of spatial topology in a toy model of classical electrodynamics in (1+1)(1+1) dimensions. The model describes a collection of Newtonian point particles coupled to a pair of scalar fields E(t,x)E(t,x) and B(t,x)B(t,x), which mediate forces between the particles and support freely propagating radiation. We formulate the model on both a line and a circle, and show that the behavior of the model strongly depends on the choice of spatial topology.