The partial anticipation of the AB effect by Ehrenberg and Siday was an approximation whose wavefunction was not singlevalued; its connection with the singlevalued AB wave involves topology: ‘whirling waves’ winding round the flux. AB is a fine illustration of idealization in physics. There are four AB effects, depending on whether the waves and the flux are classical or quantum; in the classical-classical case, fine details of the AB wavefunction have been explored experimentally in ripples scattered by a water vortex. The AB wave possesses a phase singularity, and there is a similar phenomenon in general interferometers. There are connections between the AB wave and the Cornu spiral describing edge diffraction. For bound systems, the interplay of AB and geometric phases exemplifies general aspects of degeneracies induced by varying parameters.
