The Aharonov-Bohm-Effect, Non-commutative Geometry, Dislocation Theory, and Magnetism

AbstractThe four items mentioned in the title are put into context in an informal way. 1 Introduction This is an informal paper, not intended for publication: the items mentioned in the title1. the Aharonov-Bohm effect2. non-commutative geometry3. dislocation theory, in particular concerning the role of the Burgers vector4. magnetism (mainly spin-orbit interaction)are considered and put into context. In this way we hope to remove certain high-browedfeatures from the issue, at the same time clarifying the general meaning of the first andsecond terms, and also putting some emphasis on the work of the community studying thethird or fourth one, often without relation to those working on one of the two first-mentionedsubjects. 2 The Aharonov-Bohm Effect The Aharonov-Bohm effect, see [1], is an important quantum-mechanical phenomenon show-ing explicitly that quantum-mechanics is not a classical theory as usual, for example, asNewtonian mechanics or conventional electromagnetism. A magnetic induction B~ is consid-ered, which gives rise to an interference effect of electrons, which are definitely outside therange where the Lorentz forces act and some effect could naturally be expected. Neverthe-less, a well-defined interference is observed, since in quantum mechanics it is not B~, but themagnetic vector potential A~that counts; of course, the closed-loop property of the integrationpath also counts, see below.