Aharonov–Bohm phase for an electromagnetic wave background

The canonical Aharonov–Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov–Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov–Bohm phase using both the potential (i.e. $$\oint A_\mu \mathrm{d}x ^\mu $$∮Aμd<sup>xμ</sup>) and the field (i.e. $$\frac{1}{2}\int F_{\mu \nu } \mathrm{d}\sigma ^{\mu \nu }$$12∫Fμνd<sup>σμν</sup>) forms of the Aharonov–Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space–time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov–Bohm effect could be observed.