| dbo:abstract |
Die Impulsabbildung ist ein Konzept der mathematischen Physik, mit dem das Noether-Theorem über den Zusammenhang von Symmetrien und Erhaltungsgrößen theoretisch erklärt werden kann. (de) In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various constructions of symplectic manifolds, including symplectic (Marsden–Weinstein) quotients, discussed below, and symplectic cuts and sums. (en) En géométrie symplectique, aux d'un groupe de Lie sur une variété symplectique est associée une application G-équivariante , appelée l'application moment. En un certain sens, elle généralise le moment rencontré en mécanique classique. L'application moment est définie par : où est le champ de vecteurs correspondant à l'action infinitésimale de . (fr) 심플렉틱 기하학에서 운동량 사상(運動量寫像, 영어: momentum map 모멘텀 맵[*], 영어: moment map 모먼트 맵[*])은 심플렉틱 다양체 위의 군의 작용을 생성하는 해밀토니언이다. 해밀턴 역학에서의 운동량과 각운동량을 일반화한 것이다. (ko) 在数学，尤其在辛几何中，动量映射是一个与辛流形上的李群的作用有关的工具，可用于构造作用的守恒量。动量映射推广了经典的 动量和角动量。它在各种辛流形的建立中是一个重要的部分，包括将会在后面讨论的symplectic (Marsden–Weinstein) quotients，以及s和。 (zh) |
| dbo:wikiPageExternalLink |
https://doi.org/10.1016/0034-4877(74)90021-4 https://doi.org/10.2307/2944350 http://www.numdam.org/article/SB_1985-1986__28__63_0.pdf https://archive.org/details/analysismanifold0000choq |
| dbo:wikiPageID |
3701344 (xsd:integer) |
| dbo:wikiPageLength |
14584 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1114036010 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbc:Symplectic_geometry dbr:Vector_field dbr:Interior_product dbr:Lie_group dbc:Hamiltonian_mechanics dbr:Mathematics dbr:Symplectic_cut dbr:Pullback_(differential_geometry) dbr:Momentum dbr:Lie_algebra dbr:Closed_and_exact_differential_forms dbr:Symplectic_manifold dbr:GIT_quotient dbr:Dual_space dbr:Dusa_McDuff dbr:Kostant's_convexity_theorem dbr:Quotient_space_(topology) dbr:Group_action_(mathematics) dbr:Group_cohomology dbr:Cotangent_bundle dbr:Hamiltonian_action dbr:Quantization_commutes_with_reduction dbr:Symplectic_geometry dbr:Tautological_one-form dbr:Toric_manifold dbc:Group_actions_(mathematics) dbr:Poisson_bracket dbr:Conserved_quantities dbr:Semidirect_product dbr:Kirwan_map dbr:Geometric_Mechanics dbr:Euclidean_group dbr:Exponential_map_(Lie_theory) dbr:Symplectomorphism dbr:Poisson–Lie_group dbr:Symplectic_sum dbr:Stratified_space dbr:P._B._Kronheimer dbr:S._K._Donaldson dbr:Symplectic_form dbr:1-form dbr:Coadjoint_action dbr:Coadjoint_orbit |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Cite_book dbt:Harv dbt:Reflist dbt:Isbn dbt:Issn |
| dcterms:subject |
dbc:Symplectic_geometry dbc:Hamiltonian_mechanics dbc:Group_actions_(mathematics) |
| gold:hypernym |
dbr:Tool |
| rdf:type |
dbo:Software yago:Abstraction100002137 yago:Act100030358 yago:Event100029378 yago:GroupAction101080366 yago:PsychologicalFeature100023100 yago:WikicatGroupActions yago:YagoPermanentlyLocatedEntity |
| rdfs:comment |
Die Impulsabbildung ist ein Konzept der mathematischen Physik, mit dem das Noether-Theorem über den Zusammenhang von Symmetrien und Erhaltungsgrößen theoretisch erklärt werden kann. (de) In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various constructions of symplectic manifolds, including symplectic (Marsden–Weinstein) quotients, discussed below, and symplectic cuts and sums. (en) En géométrie symplectique, aux d'un groupe de Lie sur une variété symplectique est associée une application G-équivariante , appelée l'application moment. En un certain sens, elle généralise le moment rencontré en mécanique classique. L'application moment est définie par : où est le champ de vecteurs correspondant à l'action infinitésimale de . (fr) 심플렉틱 기하학에서 운동량 사상(運動量寫像, 영어: momentum map 모멘텀 맵[*], 영어: moment map 모먼트 맵[*])은 심플렉틱 다양체 위의 군의 작용을 생성하는 해밀토니언이다. 해밀턴 역학에서의 운동량과 각운동량을 일반화한 것이다. (ko) 在数学，尤其在辛几何中，动量映射是一个与辛流形上的李群的作用有关的工具，可用于构造作用的守恒量。动量映射推广了经典的 动量和角动量。它在各种辛流形的建立中是一个重要的部分，包括将会在后面讨论的symplectic (Marsden–Weinstein) quotients，以及s和。 (zh) |
| rdfs:label |
Impulsabbildung (de) Application moment (fr) 운동량 사상 (ko) Moment map (en) 动量映射 (zh) |
| owl:sameAs |
freebase:Moment map yago-res:Moment map wikidata:Moment map dbpedia-de:Moment map dbpedia-fr:Moment map dbpedia-ko:Moment map dbpedia-zh:Moment map https://global.dbpedia.org/id/4sAG6 |
| prov:wasDerivedFrom |
wikipedia-en:Moment_map?oldid=1114036010&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Moment_map |
| is dbo:knownFor of |
dbr:Rebecca_Goldin dbr:Jean-Marie_Souriau |
| is dbo:wikiPageRedirects of |
dbr:Symplectic_reduction dbr:Hamiltonian_group_action dbr:Hamiltonian_action dbr:Moment_maps dbr:Marsden-Weinstein_reduction dbr:Marsden-Weinstein_quotient dbr:Symplectic_quotient dbr:Marsden–Weinstein_reduction dbr:Momentum_map |
| is dbo:wikiPageWikiLink of |
dbr:Mabuchi_functional dbr:Duistermaat–Heckman_formula dbr:Index_of_physics_articles_(M) dbr:Interior_product dbr:Kähler_quotient dbr:List_of_mathematical_topics_in_classical_mechanics dbr:Gauge_theory_(mathematics) dbr:Symplectic_cut dbr:Constant_scalar_curvature_Kähler_metric dbr:Symplectic_reduction dbr:Complex_geometry dbr:Delzant's_theorem dbr:Fundamental_vector_field dbr:Stability_(algebraic_geometry) dbr:Eckhard_Meinrenken dbr:Frances_Kirwan dbr:Kostant's_convexity_theorem dbr:Rebecca_Goldin dbr:Hamiltonian_group_action dbr:Isomonodromic_deformation dbr:Jean-Marie_Souriau dbr:BRST_quantization dbr:Hamiltonian_action dbr:ADHM_construction dbr:Symplectic_geometry dbr:Toric_manifold dbr:Moment_maps dbr:Marsden-Weinstein_reduction dbr:Michael_Atiyah dbr:Kirwan_map dbr:Schur–Horn_theorem dbr:Marsden-Weinstein_quotient dbr:Symmetry_in_Mechanics dbr:Symplectic_quotient dbr:Marsden–Weinstein_reduction dbr:Momentum_map |
| is dbp:knownFor of |
dbr:Jean-Marie_Souriau |
| is foaf:primaryTopic of |
wikipedia-en:Moment_map |
