Monopole (mathematics)
Encyclopedia
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 Bogomolnyi equation and be of finite action.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a monopole is a connection over a principal bundle
Principal bundle
In mathematics, a principal bundle is a mathematical object which formalizes some of the essential features of the Cartesian product X × G of a space X with a group G...
G with a section (the Higgs field) of the associated adjoint bundle
Adjoint bundle
In mathematics, an adjoint bundle is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure making the adjoint bundle into an algebra bundle...
. The connection and Higgs field should satisfy the Bogomolnyi equation and be of finite action.