Monopole (mathematics) explained

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 satisfy the Bogomolny equations and be of finite action.

See also

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

References

• Nigel Hitchin . Nigel . Hitchin . On the construction of monopoles . Communications in Mathematical Physics . 89 . 2 . 1983 . 145–190 . 10.1007/BF01211826 . 1983CMaPh..89..145H . 120823242 .
• Simon Donaldson . Simon . Donaldson . Nahm's equations and the classification of monopoles . Communications in Mathematical Physics . 96 . 3 . 1984 . 387–407 . 10.1007/BF01214583 . 1984CMaPh..96..387D . 119959346 .
• Book: Michael Atiyah

. Michael Atiyah . Michael . Atiyah . Hitchin . N. J. . Nigel Hitchin . The geometry and dynamics of magnetic monopoles . M. B. Porter Lectures . Princeton University Press . Princeton, NJ . 1988 . 0-691-08480-7 .