Geometry of the magnetic monopole

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Abstract

It is shown that the vector potential of a magnetic monopole can be obtained from consideration of the Berry phase in a new perspective. The two-component complex wavefunction can be characterized by a single CP1 projective coordinate w on the projected compactified complex plane. So the vector potential on the sphere is expressed solely in terms of w. The projective structure is more evident in this consideration. We also attempt to demonstrate that the wavefunctions can be coupled to yield a monopole with a doubling of the magnetic charge in a simple case. Generalization from a complex phase to a quaternionic phase is discussed.

Original languageEnglish
Pages (from-to)877-833
Number of pages45
JournalChinese Journal of Physics
Volume49
Issue number4
Publication statusPublished - 2011 Aug 1

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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