Three attempts for an explanation of the Aharonov–Bohm effect

The Aharonov–Bohm (A–B) effect is an effect one finds in every quantum field theory book and this is so for a very good reason. The prediction and subsequent experimental verification of the effect have been crucial cornerstones in the history of physics because they suggested that the gauge potential, also known as the Aμ field, might be interpreted as a real field, rather than just a mathematical artifact. Hence, ever since its discovery, physicists have taken it for granted that Aμ does represent something at least as tangible as any matter field. However, when one examines these arguments more closely, one realizes that attributing the status of a really existent field to the Aμ field is not as straightforward as was originally thought. But first things first: we begin with an account of the effect itself, and then attempt to give some explanation for it.

The effect

The setting for the A–B effect is very similar to the two-slit experiment, with just one difference: immediately beyond the two slits and in between them is a very fine and long solenoid, ideally infinitely long, producing a magnetic field that is confined entirely within the tube of the solenoid.