Effective Theory of Classical and Quantum Particle Dynamics in Rapidly Oscillating Fields.

We study the large-scale dynamics of charged particles in a rapidly oscillating field and formulate its classical and quantum effective theory description. The high-order perturbative results for the effective action are presented. Remarkably, the action models the effects of post-Newtonian general relativity on the motion of nonrelativistic particles, with the values of the emergent curvature and speed of light determined by the field spatial distribution and frequency.