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from Part II - Solitons and Topology; Non-Abelian Theory
Published online by Cambridge University Press: 04 March 2019
We define the Dirac monopole as a simple consequence of extending Maxwell duality to the Maxwell equations with sources, and we show that the resulting gauge fields are only defined on patches. We write formulas in terms of p-form language, and define the magnetic charge in terms of the gauge fields on patches. Then, from the quantization of the first Chern number, a topological number, we obtain Dirac quantization for the product of electric and magnetic charges. One obtains an unphysical Dirac string singularity, and its unphysical nature leads again to Dirac quantization. Finally, semiclassical nonrelativistic considerations also lead to the same Dirac quantization.
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