In the seminal works from Santos and Gozalo (Europhys Lett 45:418, 1999) and Marletto and Vedral (Phys Rev Lett 125:040401, 2020), it is shown how the Aharonov–Bohm effect can be described as the result of an exchange of virtual photons between the solenoid and the quantum charged particle along its propagation through the interferometer, where both the particle and the solenoid interact locally with the quantum electromagnetic field. This interaction results in a local and gauge-independent phase generation for the particle propagation in each path of the interferometer. Here we improve the cited treatments by using the quantum electrodynamics formalism in the Lorentz gauge, with a manifestly gauge-independent Hamiltonian for the interaction and the presence of virtual longitudinal photons. Only with this more complete and gauge-independent treatment it is possible to justify the acquired phases for interferometers with arbitrary geometries. We also extend the results to the electric version of the Aharonov–Bohm effect. Finally, we propose an experiment that could test the locality of the Aharonov–Bohm phase generation.

在Santos和Gozalo（Europhys Lett 45：418，1999）和Marletto and Vedral（Phys Rev Lett 125：040401，2020）的开创性著作中，展示了如何用交换来描述Aharonov-Bohm效应。沿螺线管和量子带电粒子在干涉仪中的传播，在螺线管和量子带电粒子之间产生虚拟光子，粒子和螺线管都与量子电磁场局部相互作用。这种相互作用导致了在干涉仪的每个路径中粒子传播的局部和量规无关的相位产生。在这里，我们通过在Lorentz规范中使用量子电动力学形式论来改进所引用的处理方法，并采用明显独立于规范的哈密顿量进行相互作用和虚拟纵向光子的存在。只有通过这种更完整且与规范无关的处理，才有可能为具有任意几何形状的干涉仪证明获得的相位。我们还将结果扩展到Aharonov–Bohm效应的电子版本。最后，我们提出了一个可以测试Aharonov–Bohm相产生的位置的实验。