The classical modeling of radiation by accelerated charged particles in pulsars predicts a cutoff in photon energy at around 25 GeV. While this is broadly consistent with observations, the classical treatment is not self-consistent, and cannot be extended to explain the rare high-energy detections of photons in the 100s of GeV range. In this paper we revisit the theoretical modeling of high-energy radiation processes in very strong electromagnetic fields, in the context of both single particles and collective plasmas. There are no classical constraints on this description. We find that there is indeed a critical energy of around 50 GeV that arises naturally in this self-consistent treatment, but rather than being a cutoff, this critical energy signals a transition from radiation that is classical to a quasiquantum description, in which the particle is able to radiate almost its total energy in a single event. This new modeling therefore places pulsar radiation processes on a more secure physical basis, and admits the possibility of the production of TeV photons in a self-consistent way.