nLab Dirac monopole

Idea

A circle bundle with connection with non-trivial first Chern class, regarded as a monopole.

For more see at flux and at Dirac charge quantization.

Properties

The trajectory of an electron in the vicinity of a magnetic monopole is (e.g. Ferraro (1956) §306) a helix on the surface of a cone in space whose vertex is the location of the magnetic monopole:

Related concepts

• Yang monopole

• fiber bundles in physics

• 't Hooft operator

References

Textbook accounts:

• V. C. A. Ferraro, §137 in: Electromagnetic Theory, The Athlone Press (1954, 1956)

• Yakov Shnir, Part I of: Magnetic Monopoles, Springer 2005 (ISBN:978-3-540-29082-7)

• Theodore Frankel, section 5.5 of The Geometry of Physics - An Introduction

See also:

• Tai Tsun Wu, Chen Ning Yang, Dirac monopole without strings: monopole harmonics, Nuclear Physics B107:3 (1976) 365–380, https://doi.org/10.1016/0550-3213(76)90143-7

• Tai Tsun Wu, Chen Ning Yang, Dirac’s monopole without strings: Classical Lagrangian theory, Phys. Rev. D 14, 437 (1976), https://doi.org/10.1103/PhysRevD.14.437