Special analytical properties of ultrastrong coherent fields

Emerging ultrastrong-laser capabilities that can reveal details of vacuum structure have intensified research into the fundamentals of quantum electrodynamics. It has been more than half a century since relativistic nonperturbative methods were introduced into the study of strong-field phenomena. Much of the early progress remains of fundamental relevance, but is known to only a small group of researchers. The aim of this paper is to reveal some of that work and to show how it impacts on current investigations. A basic result is that it has been shown that strong, single-mode fields (i.e. laser fields) can be treated by relativistic quantum mechanics with results identical to fully quantized electrodynamics. Attention is drawn to the existence of a Volkov Green’s function that has a clear physical interpretation as predicting several series of relativistic Floquet sideband states. It is more transparent and informative than the Volkov Green’s function of Schwinger. It is also shown that the fundamental experiments performed at the Stanford Linear Accelerator Center in 1997 on photon-multiphoton pair production could not be a high-order perturbative result, as was presumed by the investigators. The intensity employed was beyond the radius of convergence of perturbation theory, and the seeming perturbative increase in rate with intensity is an artifact. Of particular significance is the demonstration that a free electron in a strong plane-wave field (a “Volkov electron”) exists in an intensity-dependent superposition of angular momentum states, and is no longer a simple spin-1/2 particle.