Magnetic monopole absence

XVIII. Technical Appendix C On the Absence of Magnetic Monopoles and Currents in 0(3) Electrodynamics References... 

The absence of magnetic monopole implies the conditions V = 0 and B = -Vx = 0, which are consistent with the relations given above, since B =VAA =0. However, as with the A vector potential, the equality Bx = = Vx / 0 enables us to define a scalar potential x that can be calculated on the basis of Biot-Savart law for a filiform (filament-shaped) circuit... 

We consider now the Aharonov-Bohm effect as an example of a phenomenon understandable only from topological considerations. Beginning in 1959 Aharonov and Bohm [30] challenged the view that the classical vector potential produces no observable physical effects by proposing two experiments. The one that is most discussed is shown in Fig. 10. A beam of monoenergetic electrons exists from a source at X and is diffracted into two beams by the slits in a wall at Y1 and Y2. The two beams produce an interference pattern at III that is measured. Behind the wall is a solenoid, the B field of which points out of the paper. The absence of a free local magnetic monopole postulate in conventional... 

J. The Absence of Magnetic Monopoles V. Electromagnetism and Wave Mechanics... 

Note that, contrary to the electric multipole expansion (148), there is no zeroth order term corresponding to a magnetic charge interacting with the value of the vector potential at the expansion point, this reflecting the absence of magnetic monopoles. 

The absence of a zeroth-order moment in Eq. (5.9) reflects the fact that magnetic monopole moments do not exist. The magnetic dipole moments can thus be shown to be independent of the gauge origin Rgo (see Exercise 5.3] as a direct consequence of the absence of magnetic monopole moments. 

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