Monopole (mathematics)

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

## Physical interpretation

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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

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

## References

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* Hitchin, Nigel (1983). "On the construction of monopoles". Communications in Mathematical Physics. 89 (2): 145–190\. Bibcode:1983CMaPh..89..145H. doi:10.1007/BF01211826. S2CID 120823242.
* Donaldson, Simon (1984). "Nahm's equations and the classification of monopoles". Communications in Mathematical Physics. 96 (3): 387–407\. Bibcode:1984CMaPh..96..387D. doi:10.1007/BF01214583. S2CID 119959346.
* 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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