moment map (Q6897118)

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tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action, generalizing the classical notions of linear and angular momentum

momentum map

Language	Label	Description	Also known as
English	moment map	tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action, generalizing the classical notions of linear and angular momentum	momentum map

Statements

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defining formula

\mathrm {d} \langle \mu ,\xi \rangle |_{x}=\left(\left.{\frac {\mathrm {d} }{\mathrm {d} t}}\right|_{t=0}\exp(t\xi )\cdot x\right){\mathbin {\lrcorner }}\omega \qquad (\mu \colon M\to {\mathfrak {lie}}(G),\;x\in M,\;\xi \in {\mathfrak {lie}}(G),\;(\cdot )\colon G\times M\to M,\;\omega \in \Omega ^{2}(M))

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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Mathematics Subject Classification ID

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Microsoft Academic ID

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

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