Monopole (mathematics)

In mathematics, a monopole is a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle. The connection and Higgs field should 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. 
• Donaldson, Simon (1984). "Nahm's equations and the classification of monopoles". Communications in Mathematical Physics 96 (3): 387–407. doi:10.1007/BF01214583. 
• 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.