Symplectic frame bundle: Difference between revisions
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==Books== |
==Books== |
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* {{citation | last1=Habermann|first1=Katharina|last2=Habermann|first2=Lutz |title = Introduction to Symplectic Dirac Operators| publisher=[[Springer-Verlag]] | year=2006|isbn=978-3-540-33420-0}} |
* {{citation | last1=Habermann|first1=Katharina|last2=Habermann|first2=Lutz |title = Introduction to Symplectic Dirac Operators| publisher=[[Springer-Verlag]] | year=2006|isbn=978-3-540-33420-0}} |
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*da Silva, A.C., ''[ |
*da Silva, A.C., ''[https://people.math.ethz.ch/~acannas/Papers/lsg.pdf Lectures on Symplectic Geometry]'', Springer (2001). {{isbn|3-540-42195-5}}. {{doi|10.1007/978-3-540-45330-7}} |
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* Maurice de Gosson: ''Symplectic Geometry and Quantum Mechanics'' (2006) Birkhäuser Verlag, Basel {{isbn|3-7643-7574-4}}. |
* Maurice de Gosson: ''Symplectic Geometry and Quantum Mechanics'' (2006) Birkhäuser Verlag, Basel {{isbn|3-7643-7574-4}}. |
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Latest revision as of 00:54, 29 April 2024
In symplectic geometry, the symplectic frame bundle[1] of a given symplectic manifold is the canonical principal -subbundle of the tangent frame bundle consisting of linear frames which are symplectic with respect to . In other words, an element of the symplectic frame bundle is a linear frame at point i.e. an ordered basis of tangent vectors at of the tangent vector space , satisfying
- and
for . For , each fiber of the principal -bundle is the set of all symplectic bases of .
The symplectic frame bundle , a subbundle of the tangent frame bundle , is an example of reductive G-structure on the manifold .
See also[edit]
- Metaplectic group
- Metaplectic structure
- Symplectic basis
- Symplectic structure
- Symplectic geometry
- Symplectic group
- Symplectic spinor bundle
Notes[edit]
- ^ Habermann, Katharina; Habermann, Lutz (2006), Introduction to Symplectic Dirac Operators, Springer-Verlag, p. 23, ISBN 978-3-540-33420-0
Books[edit]
- Habermann, Katharina; Habermann, Lutz (2006), Introduction to Symplectic Dirac Operators, Springer-Verlag, ISBN 978-3-540-33420-0
- da Silva, A.C., Lectures on Symplectic Geometry, Springer (2001). ISBN 3-540-42195-5. doi:10.1007/978-3-540-45330-7
- Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006) Birkhäuser Verlag, Basel ISBN 3-7643-7574-4.