  We study the classical dynamics of many interacting particles in a
periodically driven one-dimensional (1D) system. We show that under the
rotating wave approximation (RWA), a short-distance 1D interaction ($\delta$
function or hard-core interaction), becomes a long-distance two-dimensional
(2D) interaction which only depends on the distance in the phase space of the
rotating frame. The RWA interaction describes the effect of the interaction on
the slowly changing amplitude and phase of the oscillating particles, while the
fast oscillations take on the role of a force carrier, which allows for
interaction over much larger effective distances.
