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, 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^[1] 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