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Guillemin V., Sternberg S. — Symplectic techniques in physics
Guillemin V., Sternberg S. — Symplectic techniques in physics

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Название: Symplectic techniques in physics

Авторы: Guillemin V., Sternberg S.

Аннотация:

Symplectic geometry is very useful for formulating clearly and concisely problems in classical physics and also for understanding the link between classical problems and their quantum counterparts. It is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different viewpoints. This is the first book that attempts to reconcile these approaches. The authors use the uncluttered, coordinate-free approach to symplectic geometry and classical mechanics that has been developed by mathematicians over the course of the past thirty years, but at the same time apply the apparatus to a great number of concrete problems. Some of the themes emphasized in the book include the pivotal role of completely integrable systems, the importance of symmetries, analogies between classical dynamics and optics, the importance of symplectic tools in classical variational theory, symplectic features of classical field theories, and the principle of general covariance.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 478

Добавлена в каталог: 18.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E=mc^{2}$      417 435
Action angle coordinates      356
Affine torus      351
Angle characteristic      36
Angular magnification      14
angular momentum      126 128
Astigmatism      41
Astronomical telescope      14
Barrel distortion      41
C. Neumann problem      236 378
Calogero system      381
Canonical transformations      2 25
Cartan connection      332
Circularly polarized light      118
Clean intersection      180
Coherent states      169
Coisotropic embedding theorem      315
Coisotropic immersion      176
Collective action variables      367
Collective complete integrability      359
Collective Hamiltonian      214
Collective motion      210
Coma      40
Complete integrability      349
Complex structure      160
conjugate      11
Conserved quantities      311
Constrained motion      236
Contraction      108 416
Coppersmith's theory      446
Cornu spiral      61
Covariant exterior derivative      284
Current      296
Curvature      283
Curvature of field      41
Darboux — Weinstein theorem      155
dielectric constant      131
Dielectric displacement      131
Diffraction      4 47
Dimensional reduction      291
dispersion relation      392
Distortion      41
Drop model      210 245 247
Eikonal      17
Electric field strength      131
Electromagnetic theory      131—145
Elliptically polarized      119
Energy-momentum tensor      296
Euclidean algebra      106 114
Euclidean group      105
Euler — Poisson equations      230 233
Faraday's Law of Induction      133 134 136
Fermat's principle      20 21 22 42
First focal plane      12
Focal length      12
Formal pseudodifferential operators      397
Fraunhofer diffraction      55
Free particle      78
Fresnel integrals      61
Fresnel opotics      50 54
Fresnel's formula      63 71
Galilean group      114 417 437
Gauge group      275
Gaussian Integrals      51
Gaussian optics      7
Geodesic flow on an ellipsoid      239 380
Geometric aberrations      7 38—41
Geometrical optics      34
Groenwald — van Hove Theorem      101
Hamilton's equations      45 89
Hamilton's method      17 34
Hamiltonian group action      186
Hamiltonian optics      2
Harmonic motion on a sphere      236 380
harmonic oscillator      79 91 349
Hartree — Fock      166
Heisenberg algebra      94
Heisenberg group      93
Hermite functions      80
Hermite polynomial      80
Holography      85
Holonomy      208
Infinitesimal symplectic transformations      88
Interference      4 47
Isotropic embedding      313 315
Kaehler manifolds      160 162
Kaehler structure      161
Kaehlerian vector space      161
Kinetic theory      344
Korteweg — de Vries equation      393
Kostant — Symes lemma      371
Kowalevski top      231
Lagrange top      231
Lagrangian subspace      154
Lagrangian tori      350
Left-invariant forms      169
Lie algebra cohomology      170 417
Linear holonomy      209
Linear momentum      126 128
Linear optics      5 23
Linearly polarized      117
Liquid Drop model      210
Lorentz force      140
Magnetic flux      133
Magnetic loop tension      133
Magnification      14
Marsden — Weinstein reduced space      193 198
Marsden — Weinstein reduction      192
Maxwell's equations      139
Mehler's formula      79
Metaplectic group      74
Metaplectic representation      75
Mixed characteristic      36
Moment map      184 185
Morse index theorem      23
Optical length      18 42
photoelectric effect      130
pincushion distortion      41
Planck's constant      130
Poincare group      114 441
Point characteristic      17 35
Poisson algebras      89 217
Poisson brackets      89
Polarization of light      4 5 116
Power      10
Principal bundle      272
Principal planes      16
Principle of general covariance      146 304
Projective representation      100 113
Quantization procedure      99
quantum condition      123
quantum mechanics      75
Reduced wave equation      111
Reduction      155 174
Schroedinger's equation      77
Seidel aberrations      37
Semidirect product      98 124
Semisimple Lie algebra      421
Slater determinants      165
Slice      200
Snell's law      5 10
Solitons      394
Spherical aberration      39
Spin      129
Sutherland system      385
Symmetric space      363
Symplectic diffeomorphism      2 34
Symplectic form      25 183
Symplectic group      25
Symplectic group actions      172
Symplectic induction      319
Symplectic manifold      1
Symplectic normal bundle      313
Symplectic structure      25
Symplectic transformations      25
Symplectic vector space      25
Tchapligine top      232
Thin lens      11
Thin-lens equation      13
Toda lattice      375 376
Variational derivative      402
Wave length      48
Wave packet      79
Whitehead lemmas      417
Yang — Mills field      272
Young interference experiment      5 47 48
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