Titlebook: Hamiltonian Group Actions and Equivariant Cohomology; Shubham Dwivedi,Jonathan Herman,Theo van den Hurk Book 2019 The Author(s), under exc

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https://doi.org/10.1007/978-1-4612-4646-6s that around any point of a symplectic manifold, there is a chart for which the symplectic form has a particularly nice form. In this section, we give a proof of an equivariant version of the theorem and look at some corollaries. We direct the reader to [.] or Sect.?22 of [.] for more details.

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The Physics Behind Semiconductor Technologyase space”, parametrizing position and momentum) is replaced by a vector space with an inner product; in other words, a Hilbert space (the “space of wave functions”). Functions on the manifold (“observables”) are replaced by endomorphisms of the vector space.

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The Symplectic Structure on Coadjoint Orbits,irillov–Kostant–Souriau form). An example of an orbit of the adjoint action is the two-sphere, which is an orbit of the action of the rotation group .(3) on its Lie algebra .. Background information on Lie groups may be found in Appendix.

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,The Duistermaat–Heckman Theorem,ich comes from the original article [.]) describes how the Liouville measure of a symplectic quotient varies. The second describes an oscillatory integral over a symplectic manifold equipped with a Hamiltonian group action and can be characterized by the slogan “Stationary phase is exact”.

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Geometric Quantization,ase space”, parametrizing position and momentum) is replaced by a vector space with an inner product; in other words, a Hilbert space (the “space of wave functions”). Functions on the manifold (“observables”) are replaced by endomorphisms of the vector space.

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Hamiltonian Group Actions and Equivariant Cohomology978-3-030-27227-2Series ISSN 2191-8198 Series E-ISSN 2191-8201