PM: Precision Low-Energy Quantum Electroynamic Theory and Fundamental Processes

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Seen from a general perspective, this research project deals with tiny, but important, effects which influence the spectrum of bound atomic systems, where two fundamental elementary particles circle around each other on quantum trajectories. When one combines quantum theory with relativity and adds the field quantization into the mix, then a complicated theory results, which is called quantum electrodynamics. This theory has been tested against experiment for decades, and confirmed. Recently, some interesting new effects, beyond quantum electrodynamics, may have been seen in the form of a so-called X17 particle which only couples weakly to those particles that are described by the widely-accepted Standard Model of particle physics. Effects mediated by the hypothetical new particle, visible in the spectrum of bound systems, shall be explored with high-precision calculations. This is but one of many fundamental quantum-field theoretical effects which will be studied in the context of the grant. Other effects pertain to the temperature-dependence of atom-surface interactions where the effects of so-called thermal field theory may have been seen in an experiment, and could be compared to theory for the first time. The work will be supplemented by speculative and high-risk work on overcoming the predictive limits of theoretical approaches that have set the standard for decades.The project includes the study of higher-order corrections due to quantum electrodynamic effects in atoms and higher-order corrections to the bound-electron g-factor, and the investigation of higher-order quantum electrodynamic corrections in heavy bound systems, where the orbiting particle is heavier than the electron. The latter system is of interest due to the proton radius puzzle as well as the so-called ATOMKI anomaly (which pertains to conceivable dark-photon additions to the Standard Model). The effects due to the hypothetical X17 particle are drastically enhanced in heavy as opposed to light bound systems. Complementing the quantum electrodynamic calculations, and exploring quantum field theory at high precision, fundamental temperature-dependent dynamic Casimir processes will be investigated, pertaining to atom-surface interactions, and novel techniques will be explored for the calculation of large-loop-order Feynman diagrams, conceivably overcoming current predictive limits of perturbation theory. A 770-page book on quantum electrodynamics should be completed during the award period, serving as a reference for the community. All of the above mentioned subprojects have broader significance and impacts beyond the original field of study, because of their importance for the general understanding of fundamental quantum field theory in the low-energy domain.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.