In mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle.
Physical interpretation Physically, such a monopole can be interpreted in a gauge theory coupled to a scalar field as a configuration of the scalar and gauge fields which satisfies the Bogomolny equations and has finite action. Due to the presence of a scalar field, this monopole is an example of an 't Hooft–Polyakov monopole and should not be confused with the singular monopole solutions to Maxwell's equations which are mathematically described by nontrivial principal bundles.
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. 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.