Gauge Dependence of Spontaneous Radiation Spectrum of Relativistic Atomic Beam in Non-uniform Electrostatic Field
Gauge theory requires physical observables to be gauge-independent.However,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 calculated the transient spontaneous radiation spectrum of a relativistic hydrogen atom in the non-uniform electrostatic field.Referring to our recent research on gauge dependence of spontaneous radiation spectrum in relativistic non-perturbation Coulomb field,where the radiating object is static while the charge is moving relativistically,the physical system studied in this paper is a frame-transformed version of this work.The obtained peak frequency can differ by about 330 kHz for"o-type"and 372 kHz for"π-type"or larger for the commonly used Coulomb,Lorentz,and multipolar gauges.This result is 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.
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