Thirring W.E. — Classical Mathematical Physics: Dynamical Systems and Field Theories :: Электронная библиотека попечительского совета мехмата МГУ

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Thirring W.E. — Classical Mathematical Physics: Dynamical Systems and Field Theories

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Название: Classical Mathematical Physics: Dynamical Systems and Field Theories

Автор: Thirring W.E.

Аннотация:

This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 2003

Количество страниц: 543

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\mathrm{C}^r$ vector field      138
action      100 329
Action-angle variables      116
Adiabatic theorem      235
Adjoint      46
ADM energy      459
Affine connections      300
Almost-periodic      8
Asteroids      192 197
Asymptotic completeness      128
Asymptotic fields      347
Atlas      12
Automorphism      7
Basis      294
Betatron      232
Bianchi's identity      442
Birkhoff's theorem      489
Black hole      252 292
Boundary      20
Bruns's theorem      205
Bundle atlases      30
Canonical flow      97
Canonical forms      89
Canonical transformation      61 89 90
Cartan's structure equation      440
Cauchy surface      303
Causal curve      336
Causal space      276
Causal structure      276
Center-of-mass      173
Cesaro average      102
Characteristics      301 340 463
Chart      12
Christoffel symbols      446
circular polarization      240
Closed form      296
Closed p-form      67
Codifferential      299
Collinear equilibrium      192
Comparison diffeomorphism      41
Compatible      12
complete      39
components      48
Configuration space      43
Conformal transformations      335
Conservation of angular momentum      98
Conservation of momentum      98
Constant acceleration      102
Constant of motion      42 122
Constant of motion, Euler — Lagrange      43
Constant of motion, Lagrangian      42
Constraints      6
Contracted Bianchi identity      466
Contraction      273
Contravariant      48
Convergence of flow      515
Convergence of perturbation theory      157
Cornu's spiral      414
Cosmic censorship      495
Cosmological principle      475
Cosmological term      457 480
Cotangent bundle      55
Cotangent space      46
Coulomb field      226
Coulomb potential      348
Covariant      48
Covariant differentiation      433
Covariant Lie derivative      437
Cross-angle      137
Current density      317
Curvature form      440
Cyclotron frequency      222
de Sitter metric      482
Deflection angle      122
Deflection of light by the Sun      254
Delay time      131
Delta function      305
Derivation      33
Derivative      12 25 30
Diffeomorphism      19
Differentiable      11 19
Differential      65
Differentiation      11 65
Diffraction      405
Dilatation      275
Dilatations      172
DIMENSION      12
Dipole radiation      289
Discontinuity surface      303 463
distribution      305
Domain      12
Domain of influence      336
Double pendulum      165
double stars      292
Driven oscillator      154
Dual basis      46
Dual space      46
Duality map      298
Effective potentials      184
Einstein's equations      459
Einstein's synchronization      271
Elapsed time      176
electric field      214
Electrodynamic equations of motion      214
Electromagnetic radiation      285 287
Electromagnetic waves      286
Elliptic fixed point      144
Energy momentum loss by radiation      350
Energy shell      106
Energy-momentum currents      320
Energy-momentum forms      361 389
Energy-momentum loss by radiation      375
Energy-momentum tensor      331 389
Equilateral equilibrium      192
Equilibrium positions      106
Equivalence principle      323
Ergodic theory      83
Escape criterion      200 209
Escape trajectory      82 230
Escape trajectory, Moeller transformations      188
Euclidean group      169
Euler — Lagrange equations      43
Exact form      296
Exact p-form      67
Extended configuration space      101
Extended phase space      101
Exterior differential      295
Exterior product      49 295
Fiber metric      434
Fibers      29
Fictitious forces      322
Field strength form      312
Fine structure      229
Fixed point      140
Flat      441
Flow      36 39
FORM      295
Form-valued sections      435
Frame      295
Frauenhofer region      429
Free fall      102
Free particles      169 217
Fresnel's integral      413 428
Friedmann Universe      482
future      518
Galilean group      171
Gauge group      435
Gauge theory      452
Gauge transformation      216 452
Gauss's theorem      297

General covariance      16
Generator of a canonical transformation      91
Geodesic deviation      515
Geodesic vector field      447
Geodesically complete      513
Geodesies      246
Geodetic form of the equations of motion      245
Geometric optics      408
Gravitational radiation      290
Gravitational red-shift      279
Gravitational wave      257 485
Green function      305
Green's formula      306
Group velocity      399
Half-space      19
Hamilton — Jacobi equation      103
Hamilton's equations      96
Hamiltonian      43
Hamiltonian vector field      61 93
Harmonic coordinates      456 464
Heaviside step function      303
Hedgehog      85
Helmholtz's circulation theorem      384
Hertz dipole      365
Homogeneous      470
Homogeneous stars      503
Horizon event      477
Horizon particle      477
Hyperbolic fixed point      144
Hyperbolic motion      357
Hyperbolic trajectory      223
Hypersurface      303
Imbedding theorem      15
Impact parameter      138
Incompressible      82
Infinitesimal variations      6
Integrable system      113
integral      77 78 296
Integral curve      36
Integral invariant      92
Integral of motion      105
Interior is a manifold      20
Interior product      50 52 297
Isometries      61
Isotropic      470
Jacobi's constant      191
Jacobi's identity      74
K-A-M theorem      163
Kepler problem      173
Kepler's equation      180
Kepler's third law      177
Killing vector field      61 333 447
Kirchhoff's theory of diffraction      415
Lagrangian      330
Landau — Lifshitz form      461
Laplace — Beltrami operator      299
Larmor orbits      221
Larmor's formula      288 372
Legendre transformation      43
Length of a curve      519
Lenz vector      174
Levinson's theorem      137
Lie bracket      72
Lie derivative      33 69 70 299
Lienard — Wiechert potentials      348
Lightlike      238
Lightlike coordinates      306
Linear approximation      464
Linear motion      38
Liouville measure      81
Liouville operator      33
Lissajou figure      8 110
Local canonical transformation      90
Local coordinate      15
Local flow      39
Local Lorentz transformation      456
Locally Hamiltonian vector field      93
London's equations      384
Lorentz force      214 320
Lorentz gauge      344
Lorentz transformations      217 455
Magnetic charges      314
Magnetic field      214
Manifold      6 11 12
Manifold with a boundary      19
Mass-renormalization      378
Maximally symmetric spaces      468
Maxwell's equations      215 313
Metallic boundary conditions      390
Minimal frequency      402
Minkowski space      271
Mixed fixed point      144
Moebius strip      29
Moeller transformations      125 189
n-body problem      204
Naked singularity      495
Natural basis      34 47 296
Neutron star      292
Noether's theorem      331
Nondegenerate      57
Normal modes      397
Observables      7
Oppenheimer — Snyder solution      508
Orientable      56 78 298
Orthogonal basis      51 300
Oscillator      98 118
Oscillator with a changing frequency      155
p-forms      56
Parallel at a distance      28
Parallel transport      435 439
Parallelizable      29
Partial differential equations      300
PAST      518
Peano curves      110
Pendulum      118
Penrose diagram      476
Perfect cosmological principle      475
Perturbation series      147
Perturbation theory      145
Phase space      43
Plane wave      257
Plasma frequency      386
Poincare group      217
Poincare transformations      317
Poincare's lemma      67
Poincare's recurrence theorem      82
Point-particle      321
Poisson bracket      94
Poynting's vector      335
Precession      219 252
Principle of equivalence      323
Product manifold      15
Projection to a basis      29
Proper time      519
Pseudo-riemannian      57
Pull-back      62
Quadrupole oscillations      261
Quasi-periodic orbits      110
Quasiregular singularity      523
Radiation field      374
Red-shift      279
Reduced mass      174
Regularizations      6
Reissner — Nordstroem metric      492
Reissner — Nordstrom metric      482
Renormalized equation of motion      378
Resonant cavity      401
Restricted three-body problem      190
Restriction      296
Retarded Green function      342

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