Monopole (mathematics)

In mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle.

Physical interpretation

Physically, the section can be interpreted as a Higgs field, where the connection and Higgs field should^[why?] satisfy the Bogomolny equations and be of finite action.

See also

• Nahm equations
• Instanton
• Magnetic monopole
• Yang–Mills theory

References

• Hitchin, Nigel (1983). "On the construction of monopoles". Communications in Mathematical Physics 89 (2): 145–190. doi:10.1007/BF01211826. Bibcode: 1983CMaPh..89..145H. 
• Donaldson, Simon (1984). "Nahm's equations and the classification of monopoles". Communications in Mathematical Physics 96 (3): 387–407. doi:10.1007/BF01214583. Bibcode: 1984CMaPh..96..387D. http://projecteuclid.org/euclid.cmp/1103941858. 
• Atiyah, Michael; Hitchin, N. J. (1988). The geometry and dynamics of magnetic monopoles. M. B. Porter Lectures. Princeton, NJ: Princeton University Press. ISBN 0-691-08480-7. 

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