Problems with the Aharonov-Bohm Theory

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A list of theoretical problems concerning the Aharonov-Bohm (AB) theory is presented together with links to papers and pages that discuss them in detail.
  1. The phase depends on all coordinates of the system. Each term of the full wave function has its own phase. For a discussion, Click here.
  2. For having an AB effect, it is mandatory that the source of the potential behaves like an inert object throughout the process. For a discussion, Click here.
  3. The previous condition does not hold in the case of the electric AB effect. Here the single particle treatment is inconsistent with energy conservation. For a discussion, Click here.
  4. An example can be shown where the AB multiply connected field free region exists but the AB phase shift disappears.

    For a short discussion, Click here.

     For a more comprehensive discussion, Click here.
  5. It can be shown that AB do not prove that topology in general and multiply connected field free regions in particular, play an inherent role in quantum mechanics. For a discussion, Click here.
  6. The action extremum and its implications on the AB effects. For a discussion, Click here.