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Symplectic techniques in physics

Author: Victor Guillemin; Shlomo Sternberg
Publisher: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Genre/Form: Symplektische Methode
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Victor Guillemin; Shlomo Sternberg
ISBN: 0521248663 9780521248662
OCLC Number: 9686498
Description: xi, 468 pages : illustrations ; 24 cm
Contents: Gaussian optics --
Hamilton's method in Gaussian optics --
Fermat's principle --
From Gaussian optics to linear optics --
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations --
Fermat's principle and Hamilton's principle --
Interference and diffraction --
Gaussian integrals --
Examples in Fresnel optics --
The phase factor --
Fresnel's formula --
Fresnel optics and quantum mechanics --
Holography --
Poisson brackets --
The Heisenberg group and representation --
The Groenwald-van Hove theorem --
Other quantizations --
Polarization of light --
The coadjoint orbit of a semidirect product --
Electromagnetism and the determination of symplectic structures --
Epilogue: Why symplectic geometry? --
The geometry of the moment map --
Normal forms --
The Darboux-Weinstein theorem --
Kaehler manifolds --
Left-invariant forms and Lie algebra cohomology --
Symplectic group actions --
The moment map and some of its properties --
Group actions and foliations --
Collective motion --
Cotangent bundles and the moment map for semidirect products --
More Euler-Poisson equations --
The choice of a collective Hamiltonian --
Convexity properties of toral group actions --
The lemma of stationary phase --
Geometric quantization --
Motion in a Yang-Mills field and the principle of general covariance --
The equations of motion of a classical particle in a Yang-Mills field --
Curvature --
The energy-momentum tensor and the current --
The principle of general covariance --
Isotropic and coisotropic embeddings.
Responsibility: Victor Guillemin, Shlomo Sternberg.
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