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

"Antileibnitz" rule      206
$C^{k}$ -manifold      112
$C^{r}$ at x      114
$C^{r}$ differentiable      115
$C^{r}$ mapping      115
$L^{1}$ spaces      52
$L^{p}$ space      53
$L^{\infty}$ spaces      56
$V^{4}$       333
$W_{p}^{m}(\mathbb{R}^{n})$       488
$\Delta$       296 317
$\mathscr{C}^{m}(\bar{U})$       29
$\mathscr{D}(R^{n})$       488
$\mathscr{P}$ -topology      424
$\sigma$ -field      33
$\sigma$ -finite      36
$\sigma$ -ring      33
a.e.      36
Abelian group      7
Absolute differential      301 371
Absolute integral invariant      263
Accumulation point      13
Active viewpoint      406
Ad G invariant      390
Adjoint map      168 181
Adjoint representation      168 184
Adjoint theorem      63
Admissible atlas      543
Admissible map      368
Affine      10
Affine geodesic      302
Affine group      157
Affine parameter      303
Alexandroff theorem      36
Algebra      9
Algebra, Clifford      65 176 416
Algebra, convolution      459 462
Algebra, differential graded      202
Algebra, Dirac      65
Algebra, exterior      196
Algebra, graded      202
Algebra, Grassman      196
Algebra, Lie      134 156 172
Algebra, Pauli      65
Algebra, tensor      140
Algebraic dual      10
Algebraically equivalent      22
Almost complex      331
Almost everywhere      213
Almost hermitian      334 398
Almost kaehlerian      398
Ambrose Singer      381
Analytic manifold      112
Antiderivation      205
Antiselfdual      414
Arc length      320
Arcwise connected      19
Ascoli — Arzela theorem      61
Associated bundle      367 383
Associated Pfaff system      237
Associated space of ideal      233
Associated space Q*      230
Associated topology      20
Associated vector bundle      367
Atiyah — Singer theorem      396
Atlas      111 543
Atlas, admissible      543
Atlas, compatible      543
Atlas, equivalent      112 543
Atlas, examples      186 190
Automorphism      156 174
Auxiliary functions      194
Average formula      501
Baire space      25
Ball      23
Banach algebra      59
Banach manifold      112 543
Banach space      28
Banach theorem      18
Base      14 22
Base (Top, vector space)      21
Base (topological)      14
Base of a bundle      124
Base of neighborhoods      14
Base, orthonormal      31
Basic vector field      378
Basis for $A^{p}(X)$       197
Basis in $T_{x}(X)$ (moving frame)      134
Basis in $T_{x}^{*}(X^{n})$       136
Basis, Hamel      9
Basis, natural      119 136
Basis, orthonormal      287
Bel — Robinson tensor      340
Betti numbers      224
Bianchi identities      307 309 310 375
Bicharacteristics      252
Bidual (of a Banach space)      59
Bijection      3
Bolzano — Weierstrass theorem      15
Boolean algebra      33
Borel $\sigma$ -field      597
Borel measure      36
Borel sets in $\mathbb{R}$       34
Borsuk's theorem      562
Bound      5
Bound, greatest lower      5
Bound, least upper      5
Bound, lower      5
Bound, upper      5
Boundary      218 222
Boundary-value problems      502
Bounded distributions      525
Bounded linear operator      57
Bounded set      23
Brouwer fixed point theorem      562
Bundle      124
Bundle category      127
Bundle homomorphism      380
Bundle morphism      127
Bundle, cotangent (fibre)      138 545
Bundle, differentiable fibre      127
Bundle, fibre      125
Bundle, frame      129
Bundle, principal fibre      129
Bundle, tangent (fibre)      129 545
Bundle, trivial      125
Bundle, vector      125
C* algebra      59
Calculus of variations      83
Canonical coordinates (one parameter subgroup)      161 184 187
Canonical form      169
Canonical gaussian measure      581
Canonical isomorphism G and $V_{p}$       360
Canonical isomorphism on riemannian manifolds      286
Canonical symplectic form      554
Canonical transformation      267
Cardinality      3
Cartan structural equations      306 373 376
Cartesian product      2
Catastrophe      280
Category      3
Cauchy characteristic manifolds      259
Cauchy net      23
Cauchy problem      256 278
Cauchy sequence      23 25
Cauchy sequence of step maps      51
Cauchy — Kovalevski theorem      493
Cauchy — Schwarz inequality      11
Causal structures      350
Caustics      100

Center (of the group)      7
Characteristic class      390
Characteristic function      1
Characteristic manifold      250 492
Characteristic strips      252
Characteristic system      250 277
Characteristic vector      250
Charge quantization      408
Chart      111
Chern character      393
Chern class      393
Chern number      396
Christoffel symbols      301 366
class      79
Clifford algebra      64 176 416
Closed (differential system)      238
Closed form      222
Closed graph theorem      63
Closed map      63
Closed sets      13
Closure      13
Closure (differential system)      238
Cluster point      15
Coarser (topology)      12
Cobasis      136
Coboundary      200 222
Cocycle      222
Coercive (bilinear form)      507
Cohomology      222
Cokernel      401
Collection      1
Commutative group      7
Compact      15
Compact (mapping)      61 564
Compact cohomology      225
Compact support      225
Compact, locally      16
Compact, relatively      16
Compactification      16
Compactified Minkowski space      338
Compatible      543
Complement      2
Complementable split      549
Complementary      9
Complete integrability      243 253
Complete metric space      25
Complete system of exterior equations      232
Complete topological vector space      23
Complete, geodesically      326
Complete, sequentially      23
Completion      25
Complex analytic manifold      112
Complex line as frame      333
Complex measure      49
Complex structure      331 552
Components of a tangent vector      118
Composite mapping      2
composition      3
Compound matrices      270
Condimension      10
Cone property      492
Configuration space      169 265
Configuration space time      265
Conformal automorphisms      350
Conformal spaces      350 354
Conjugate points      87 100 344
Conjugate variables      169
Connected      16
Connected, arcwise      19
Connected, locally      17
Connected, locally arcwise      19
Connected, locally simply      19
Connected, simply      19
Connection coefficients      301
Connection forms      301 362 364 371
Connection on a principal fibre bundle      330 333
Connection, existence of      308
Connection, linear      300
Connection, metric      300
Connection, Riemannian      308
Conservation of energy theorem      555
Constant mapping      4
Continuous mapping      17
Continuous spectrum      60
Contracted multiplication (tensor)      141
Contracting mapping theorem      88 89
Contraction (tensor)      141
Contravariant functor      4
Contravariant spinor      418
Convergence      15
Convergence (in) $\mathscr{D}^{m}$ and $\mathscr{D}$       430
Convergence (in) measure      41
Convergence criterion in $\mathscr{D}'$       454
Convergence in the mean      54
Convergence, strong      29
Convergence, uniform      28
Convergence, weak      30
Convex      10
Convex, locally      22
Convolution algebra      459 462
Convolution of distributions      462
coordinates      111
Coordinates, canonical      161
Coordinates, local      111
Coordinates, local (forms)      197
Coordinates, normal      161
Coset      7
Coset, left      7
Coset, right      7
Cotangent bundle      138
Cotangent space      545
Cotangent vector space      136
Countable      3
Countable set      3
Countable, first      14
Countable, second      14
Countably additive      35
Covariant derivative      301 302 367 370 372 418
Covariant exterior derivative      372
Covariant functor      4
Covariant gauge derivative      403
Covariant spinor      418
Covariant tensor      546
Covariant vector      545
Covariant vector field      138
Covering      15
Covering space      19
Critical neck theorem      572
Critical point      119 546 547
Critical value      546 547
Cross-section      132
Current      228 484
Curvature      305 306 372
Curvature forms      299 306 372 378
Curvature scalar      310
Curvature tensor      306
Curvature, extrinsic      314
Curve, geometric      262
Curve, integral      144
Curve, parametrized      120
CYCLE      222
Cylindrical $\sigma$ -field      576 594
Cylindrical function      578
Cylindrical measures      573 576
Cylindrical subset      576
Darboux theorem      281
De Rham cohomology      223
de Rham theorem      226
Degree      556 557
Degree of a compact perturbation of Id      564

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