Nonperturbative quantum electrodynamics in the Cherenkov effect

Quantum electrodynamics (QED) is one of the most precisely tested theories in the history of science, giving accurate predictions to a wide range of experimental observations. Recent experimental advances allow for the ability to probe physics on extremely short attosecond timescales, enabling ultrafast imaging of quantum dynamics. It is of great interest to extend our understanding of short-time quantum dynamics to QED, where the focus is typically on long-time observables such as 𝑆 matrices, decay rates, and cross sections. That said, solving the short-time dynamics of the QED Hamiltonian can lead to divergences, making it unclear how to arrive at physical predictions. We present an approach to regularize QED at short times and apply it to the problem of free-electron radiation into a medium, known as Cherenkov radiation. Our regularization method, which can be extended to other QED processes, is performed by subtracting the self-energy in free space from the self-energy calculated in the medium. Surprisingly, we find a number of previously unknown phenomena yielding corrections to the conventional Cherenkov effect that could be observed in current experiments. Specifically, the Cherenkov velocity threshold increases relative to the famous conventional theory. This modification to the conventional theory, which can be non-negligible in realistic scenarios, should result in the suppression of spontaneous emission in readily available experiments. Finally, we reveal a bifurcation process creating radiation into new Cherenkov angles, occurring in the strong-coupling regime, which would be realizable by considering the radiation dynamics of highly charged ions. Our results shed light on QED phenomena at short times and reveal surprising new physics in the Cherenkov effect.