  The long-standing challenge to describing charged particle dynamics in strong
classical electromagnetic fields is how to incorporate classical radiation,
classical radiation reaction and quantized photon emission into a consistent
unified framework. The current, semiclassical methods to describe dynamics of
quantum particles in strong classical fields also provide the theoretical
framework for fundamental questions in gravity and hadron-hadron collisions,
including Hawking radiation, cosmological particle production and
thermalization of particles created in heavy-ion collisions. However, as we
show, these methods break down for highly relativistic particles propagating in
strong fields. They must therefore be improved and adapted for the description
of laser-plasma experiments that typically involve the acceleration of
electrons. Theory developed from quantum electrodynamics, together with
dedicated experimental efforts, offer the best-controllable context to
establish a robust, experimentally-validated foundation for the fundamental
theory of quantum effects in strong classical potentials.
