About: Bogomolny equations

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In mathematics, and especially gauge theory, the Bogomolny equation for magnetic monopoles is the equation where is the curvature of a connection on a principal -bundle over a 3-manifold , is a section of the corresponding adjoint bundle, is the exterior covariant derivative induced by on the adjoint bundle, and is the Hodge star operator on . These equations are named after E. B. Bogomolny and were studied extensively by Michael Atiyah and Nigel Hitchin.

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rdf:type	soccer club season
rdfs:label	Bogomolny equations (en) 보고몰니 방정식 (ko) Equações de Bogomolny (pt)
rdfs:comment	양자장론에서 보고몰니 방정식(Богомольный方程式, 영어: Bogomol’nyi equation)은 3차원 공간 위의 주접속과 딸림표현 스칼라장에 대한 1차 비선형 편미분 방정식이다. 그 해는 자기 홀극을 나타낸다. (ko) Em matemática, as equações de Bogomolny para monopólos magnéticos são as equações FA = DAφ, onde FA é a curvatura de uma conexão A em um fibrado G sobre uma variedade tridimensional M, φ é uma seção do correspondente e é o em M. Essas equações são nomeadas em homenagem a E. B. Bogomolny. As equações são uma redução dimensional das equações auto-duplas de Yang-Mills em quatro dimensões e correspondem aos mínimos globais da ação apropriada. Se M estiver fechado, existem apenas soluções triviais (isto é, planas). (pt) In mathematics, and especially gauge theory, the Bogomolny equation for magnetic monopoles is the equation where is the curvature of a connection on a principal -bundle over a 3-manifold , is a section of the corresponding adjoint bundle, is the exterior covariant derivative induced by on the adjoint bundle, and is the Hodge star operator on . These equations are named after E. B. Bogomolny and were studied extensively by Michael Atiyah and Nigel Hitchin. (en)
dcterms:subject	Differential geometry Magnetic monopoles
Wikipage page ID	35175454 (xsd:integer)
Wikipage revision ID	1117597988 (xsd:integer)
Link from a Wikipage to another Wikipage	Monopole moduli space Hodge star operator Curvature form Differential geometry Magnetic monopoles Connection (mathematics) Mathematics Gauge theory (mathematics) Magnetic monopole Bogomol'nyi–Prasad–Sommerfield bound Adjoint bundle Ginzburg–Landau theory 3-manifold Exterior covariant derivative Nigel Hitchin Michael Atiyah Seiberg–Witten theory Yang–Mills equations Principal bundle
sameAs	Bogomolny equations Bogomolny equations Bogomolny equations Bogomolny equations Bogomolny equations Bogomolny equations
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description dbt:Differential-geometry-stub dbt:Eom dbt:Mathapplied-stub
has abstract	In mathematics, and especially gauge theory, the Bogomolny equation for magnetic monopoles is the equation where is the curvature of a connection on a principal -bundle over a 3-manifold , is a section of the corresponding adjoint bundle, is the exterior covariant derivative induced by on the adjoint bundle, and is the Hodge star operator on . These equations are named after E. B. Bogomolny and were studied extensively by Michael Atiyah and Nigel Hitchin. The equations are a dimensional reduction of the self-dual Yang–Mills equations from four dimensions to three dimensions, and correspond to global minima of the appropriate action. If is closed, there are only trivial (i.e. flat) solutions. (en) 양자장론에서 보고몰니 방정식(Богомольный方程式, 영어: Bogomol’nyi equation)은 3차원 공간 위의 주접속과 딸림표현 스칼라장에 대한 1차 비선형 편미분 방정식이다. 그 해는 자기 홀극을 나타낸다. (ko) Em matemática, as equações de Bogomolny para monopólos magnéticos são as equações FA = DAφ, onde FA é a curvatura de uma conexão A em um fibrado G sobre uma variedade tridimensional M, φ é uma seção do correspondente e é o em M. Essas equações são nomeadas em homenagem a E. B. Bogomolny. As equações são uma redução dimensional das equações auto-duplas de Yang-Mills em quatro dimensões e correspondem aos mínimos globais da ação apropriada. Se M estiver fechado, existem apenas soluções triviais (isto é, planas). (pt)
gold:hypernym	FA
prov:wasDerivedFrom	wikipedia-en:Bogomolny_equations?oldid=1117597988&ns=0
page length (characters) of wiki page	2189 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bogomolny_equations
is Link from a Wikipage to another Wikipage of	Monopole (mathematics) Monopole moduli space Gauge theory (mathematics) Magnetic monopole Bogomol'nyi–Prasad–Sommerfield bound Yang–Mills equations Nahm equations Bogomolny equation
is Wikipage redirect of	Bogomolny equation
is foaf:primaryTopic of	wikipedia-en:Bogomolny_equations

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