nLab
Aharonov-Bohm effect

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The Aharonov-Bohm effect is an observable property of the electromagnetic field which shows that the electromagnetic field strength differential 2-form FF alone does not characterize the physically distinguishable field configurations, but that only the “vector potential” of the field strength does, hence the circle bundle with connection of which which FF is the curvature 2-form.

Accoridngly, the Aharonov-Bohm effect is a certain interference pattern in the wavefunction of an electron that propagates in an electromagnetic background gauge field that is modeled by a circle bundle with connection which is a flat connection, hence has vanishing curvature/field strength just as the trivial electromagnetic field configuration does, but which is nevertheless a nontrivial connection. The observed interference comes from the holonomy of this non-trivial but flat connection around loops in spacetime which represent non-trivial elements of the fundamental group.

Created on November 9, 2012 17:27:46 by Urs Schreiber (80.187.201.44)