Gauge dependence of spontaneous radiation spectrum of relativistic atomic beam under non-uniform electrostatic field

TL;DR

This paper investigates the gauge dependence of the spontaneous radiation spectrum of a relativistic hydrogen atom in a non-uniform electrostatic field, revealing significant differences in peak frequencies across gauges with implications for theory and experiments.

Contribution

It demonstrates the gauge dependence of the spontaneous radiation spectrum in a relativistic atomic system, highlighting the importance of gauge choice in theoretical and experimental contexts.

Findings

Peak frequency differences up to 413 KHz across gauges

Gauge choice affects the accuracy of atomic clock timing

Results emphasize the need for gauge-consistent calculations in quantum systems

Abstract

Gauge theory requires physical observables to be gauge-independent. However, ever since Lamb noticed the problem of gauge selection in calculating atomic spontaneous radiation spectrum, the problem of gauge dependence was encountered in many fields of physics research. Therefore, it is important to test the self-consistency of gauge symmetry for various physical systems. In this paper, we calculate the transient spontaneous radiation spectrum of a relativistic hydrogen atom in the non-uniform electrostatic field under the atomic self-reference frame. The physical system studied in this paper is a frame-transformed version of our recent work [\href{https://link.springer.com/paper/10.1140/epjd/s10053-022-00407-5}{Euro. J. Phys. D \textbf{76}, 84(2022)}] where the radiating object is static while the charge is moving relativistically. The obtained peak frequency can differ by about $413$ $\mathrm{KHz}$ or larger for the commonly used Coulomb, Lorentz, and multipolar gauges. This observation can be significant not only for studying how the gauge field interacts with the quantum system in theory, but also for practical experimental applications, such as the timing accuracy of atomic clocks in the external electromagnetic field.