Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M. — Analysis, manifolds and physics. Part I. :: Электронная библиотека попечительского совета мехмата МГУ

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Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M. — Analysis, manifolds and physics. Part I.

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Название: Analysis, manifolds and physics. Part I.

Авторы: Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M.

Аннотация:

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 660

Добавлена в каталог: 03.11.2012

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Предметный указатель

Degree of a derivation      206
Degree of a differential operator      202
Degree of a form      195 551
Degree of a mapping      221 556
Degree of an antiderivation      206
Density theorem      434 488
Derivation      118 205
Derivative      71
Derivative covariant      295 301 302
Derivative, directional covariant      302
Derivative, distributions      446
Derivative, exterior      200 317
Derivative, exterior covariant      372
Derivative, Lie      134
Derivative, Pfaff      138
Diagonal system      520
diagonalisation      521
Diffeomorphism      74 115 547
Difference (subset)      2
Difference, symmetric      2
Differentiable at a point      71
Differentiable fibre bundle      127
Differentiable function      113 544
Differentiable in U      73
Differentiable manifold      112 543
Differentiable tangent bundle      128
Differential      71
Differential at a point      71 121 546
Differential equation with constant coefficient      469
Differential equations      94
Differential form      195
Differential graded algebra      202
Differential mapping      71 121
Differential operator      202
DIMENSION      10
Dirac algebra      65 416
Dirac distribution      439 448
Dirac kernels      533
Dirac matrices      176
Dirac measure      438
Dirac measure on a surface      438
Dirac p-current      439
Direct product of distributions      445
Direct product of manifolds      114
Direct sum      9
Directed set      5
Direction      293
Dirichlet problem      92 502
Discrete      12
Disjoint      2
Distance      23
distribution      435
Distribution on a paracompact $C^{\infty}$ manifold      480
Distribution transformation under a diffeomorphism      457
Distribution with compact support      442
Distribution, bounded      525
Distribution, convolution      462
Distribution, derivation      446
Distribution, direct product      445
Distribution, division      444
Distribution, equal      440
Distribution, inverse derivative      450
Distribution, order      439
Distribution, positive      495
Distribution, regularization      465
Distribution, subharmonic      496
Distribution, support      441
Distribution, tempered      476
Distribution, tensor      482
Divergence      317
Domain      2
Domain of dependence      515
Domain of integration      217
Dual      10
Dual, algebraic      10
Dual, star      283 319
Dual, topological      22
Duality      225
Dynamical systems      144
Effectively      153
Egorov theorem      40
Eigenvalue      60
Eigenvector      60
Eikonal equation      535
Einstein tensor      310 315
electromagnetic field      263 271 336
Electromagnetic potential      366
Electromagnetic shock waves      535
Elementary "solutions"      468
Elementary domain of integration      217
Elementary kernel      472
Elementary kernels of the harmonic oscillator      538
Elementary p-chain      217
Elementary solutions of the heat equation      510
Elementary solutions of the wave equation      511 538
Elliptic (bilinear forms)      507
Elliptic complex      397
Elliptic equations      494
Elliptic operator      397
Embedding      241 550
Empty      1
Endomorphism      174
Energy      321
Energy density      338
Energy function      87 344
Energy inequality      514
Energy integral      324 489 513
Equation of convolution      466
Equation of geodetic deviation      343
Equicontinuous      61
Equipotent      3
Equivalence class      5
Equivalence relation      5
Equivalence, atlases      112
Equivalence, fibre bundle      125
Equivariance      373
Euclidean space      299
Euler class      394
Euler equation      76 77
Euler number      395
Euler — Lagrange equation      171
Euler — Poincare characteristic      293 395
Exact form      222
Exact sequence      397
Existence and uniqueness diff. eq. (lipschitzian case)      97
Exponential mapping      160 181 325
exponentiation      344
Extension of the mapping      3
Extension theorem      425
Exterior algebra      196
Exterior covariant derivative      372
Exterior derivative      200 317
Exterior differential form      195 551
Exterior differential systems      229
Exterior equations      229
Exterior product      196 551
External operation      6
f-distribution associated with the function      437
Factor group      7
Faithful      162
Family      1
Fatou lemma      42
Fermi geodetic system      345 349
Feynman diagram technique      596 598
Feynman — Green function      100
Fibered structure      384
Fibre at x      125
Fibre bundle      125
Fibre coordinates      127
Fibre, typical      125

Field      8
Field of subset      33
Field strength      375
Filter      14
Finer (topology)      12
Finite dimensional perturbation      563
Finite measure      36
Finitely additive      35
Finitely valued      41
First countable      14
First fundamental form      291
First integral      243
First order differentiable equation      250
First order partial differential equation      250 277
Fischer Riesz theorem      52
Flat connection      373
Flat space      299
Flow      144
FORM      10 138 142 195
Form, vector valued      210
Fourier transform      474 531 532 579
Frame      128 134
Frame bundle      128 193 376
Frechet differential      71
Frechet space      26
Fredholm alternative      62
Fredholm operator      401
Freely      153
Friedrichs lemma      489
Frobenius theorem      243 245 248
Fubini theorem      45
Function      2
Function $C^{r}$       114 544
Function, characteristic      1
Function, coordinate      114
Function, differentiable      113 544
Function, finitely valued      41
Function, integrable      42
Function, measurable      40
Function, numerical      2
Function, set      34
Function, simple      40
Function, step      41
Functional      10
Functional derivative      72
functor      4 116
Functor, contravariant      4
Functor, covariant      4
Fundamental 2-form      334
Fundamental form, first      290
Fundamental form, second      292
Fundamental group      19
Fundamental vector      339
Future compact      524
Future directed      288
Gauge covariant derivative      403
Gauge field      402 403
Gauge group      402
Gauge potential      402
Gauge principles      402
Gauge transformation      405
Gauge, Lorentz      337
Gauss Bonnet theorem      395
Gauss normal coordinates      315
Gauss — Codazzi      315
Gaussian promeasures      582
General potential formula      501
Generating function      267
Generator      146
Generic points      238
Geodesic      302 320 321 323
Geodesic flow      325
Geodesically complete      326
Geodetic deviation      87 346
Geodetic motion      344
Geometric curve      262
Geometric sum      9
Germ      118 544
Global gauge transformation      402
Global inner product      296
Global inverse function theorem      93
Global transformation      145
Globally hyperbolic      517
Graded algebra      197 202
Graph      64
Grassman algebra      196
Gravitational radiation      336
Green formula      499 527
Green function      503
Group      7
Group manifold      182
Group of rotations      181
Group of transformations      143 152
Group SO(3), SU(2)      181
Group, $GL(n,\mathbb{C})$       172
Group, $GL(n,\mathbb{R})$       117 128 172
Group, abelian      7
Group, action      126 162
Group, causal      352
Group, center of      7
Group, cohomology      223
Group, commutative      7
Group, conformal      352
Group, factor      7
Group, fundamental      19
Group, homology      223
Group, Lie      116 152
Group, local      117 145
Group, Lorentz      290
Group, one parameter      117 158
Group, pseudo      145
Group, quotient      7
Group, structural      125
Group, topological      21
Haar measure      39
Hahn extension theorem      35
Hahn — Banach theorem      424
Hamel basis      9
Hamilton equations      272
Hamilton — Jacobi equation      272 277
Hamiltonian      169 269
Hamiltonian system      267
Hamiltonian vector space      265 269 272
Handle      572
Harmonic      318
Hausdorff topological space      13
Heat diffusion      496
Heaviside function      447
Heine — Borel theorem      16
Hermitian metric      334
hessian      80 571
Higgs field      404
Hilbert manifold      112 555
Hilbert space      30
Hilbert — Schmidt operator      62
Hilbert — Schmidt theorem      63
Hilbertian methods      505 507
Holder inequality      53
Holonomy bundle      387
Holonomy group      381 387
Homeomorphism      18
Homologous      223
Homology      222
Homology class      223
Homomorphism      7
Homotopic      20 185
Hopf — Rinow theorem      330
Horizontal      358 373 378
Horn      3
Hull      17

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