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Choquet-Bruhat Y., Dewitt-Morette C. — Analysis, Manifolds and Physics (vol. 2)
Choquet-Bruhat Y., Dewitt-Morette C. — Analysis, Manifolds and Physics (vol. 2)

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Название: Analysis, Manifolds and Physics (vol. 2)

Авторы: Choquet-Bruhat Y., Dewitt-Morette C.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 449

Добавлена в каталог: 22.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H_{s,\delta}(\mathbb{R}^{n})$ spaces      396
$H_{s}(S^{n})$ spaces      396
$Pin^{+}(n)$      25
$Pin^{-}(n)$      25
$\gamma_{+}(n,m)$      21
$\gamma_{-}(n,m)$      21
$\sigma$-models      274
(auto-) Baecklund transformation      179
(Gateaux) derivative      51 354
(geometrical simplicial) complex      128
(space time) parity operator      18
A-valued connections      122
A-valued covariant vectors      122
A-valued metrics      122 125
A-valued spinors      122
A-valued tangent vectors      124
Abelian representations of nonabelian groups      110
Abelianization      111
Abstract simplex      138
Abstract simplicial complex      138
Adjoint      47
Adjoint representation      365
Adler — Kostant — Symes theorem      219 229—231
Almost complex      294
Almost Kaehler      299
Analytic diffeomorphism      241
anomalies      349 361
Antihomomorphisms of a Lie algebra      102
Arnold's theorem      219
Associated polyhedron      128
Atiyah — Singer index theorem      321
B-valued covariant vector      125
B-valued metric g      125
Back face      132
Baecklund transformations      178 183
Baecklund transformations for evolution equations      181
Ball of $W^{p}_{s}$ in $W^{p}_{s-1}$      398
Berezin integral      57
Berezin integration      57
Berezinian      4
Betti numbers      321 324—326
Bianchi identity      340
Bianchi — Lie transformation      183
Bockstein map      149
body      2
Bonnet equation      183
Bound states      425
Boundary      129 138
Boundary of a chain      129
Boundary of a simplex      128
Broken symmetry      310
BRST operator      363
Bundle classification      335
Bundle homomorphism      335
Bundle reduction      310
C.W. complexes      158
Calahi — Yau spaces      294
Campbell — Hausdorff expansion formula      354
Canonical commutation relations      167
Canonical Poisson structure      217
Canonical spin structure      154
Cartan — Killing form      93
Casimir functions      185 186 213
Cauchy problem      275
Cayley inner product      265
Cayley norm      265
Cayley numbers      264
Cech homology      138
Central extension of a group      166
Cep product      132
Characteristic classes      321 339
Characteristic matrix      254
Characteristic space      192
Characters      114
Charge conjugation      27 30
Chern — Simons classes      340 342
Chern — Simons form      346
Classifying maps      337
Clifford algebra as a coset of the tensor algebra      14
Clifford algebras      6
Clifford group      18 22
Closed operator      48
Coadjoint orbits      218
Coadjoint orbits in G      207
Coadjoint representation      365
Coboundary      131 159
Coboundary operator      159 168 364
Cochain      158
Cochains on G      168
Cocycle      132 159 187
Cocycle condition      161 162
Cocycles on the Lie algebra of a gauge group      349
Coframe      289
Cohomology      127 132
Cohomology group of G with values in an abelian group      159
Cohomology of groups      158
Cohomology of Lie algebras      167
Commutant      114
Commutator subgroup      110
Compact spaces      39
Compactness in weak star topology      40
Completely integrable      192 288
Completely integrable systems      219
Completeness      398
COMPLEX      128
Complex manifold      295
Composition of maps      281
Composition theorem      387 431
Cone property      379
Conformal system for Einstein equations      249
Conformal transformation      244
Conformal transformation of nonlinear wave equations      256
Conjugate ghost field operator      370
Connections on a Spin bundle      156
Conserved current      69
Constant cocycle      133
Continuous spectrum      48
Contractible maps      44
Contractible to a point      337
Cosimplex cochain      131
Cospinor      36 135
Cotangent vector      124
Covariant codifferential      253
Critical point      278
Current algebra      350
Curvature integral      332
Cycles      129
de Rham theorem      321
Degree of a Pin group element      146
Density theorem      430
DeWitt algebra      1 119
Differentiable submanifolds      91
Differential      275
Differential equations as exterior differential system      173
Dimension of a complex      128
Dimension of a simplex      127
Dimension of chains      128
Dirac adjoint      36
Dirac operator      244
Direct products      95
Distribution with laplacian in $L^{2}(R^{n})$      399
Dolbeault differential      298
Dolbeault operators      297
Dual of a Lie algebra      187
Dual pair      213
EDGE      127
Eigenspace      48
Eigenvalue      48
Einstein cylinder      244
Einstein equations      249 311 408
Einstein equations with sources      413
Einstein vacuum      311
Einstein — Yang — Mills equations      286
Elementary solution of the wave equation      373
Embedding      92 283
Energy      311
Energy density      276
Energy density of the Yang — Mills field      89
Energy functional      277
Energy of a field      72
Energy with respect to a timelike vector field      83
Equivalent bundles      334
Equivalent spin structures      151
Equivariant momentum mapping      214
Essential spectrum      49
Euclidean at infinity      430
Euler class      321 330
Euler equations      76
Euler numbers      321 324
Euler — Lagrange equations for a Dirac particle      80
Euler — Poincare characteristic      321
Euler — Poincare number      329
Even matrix      3
Even vector      124
Extension of a group      164
Extension of SO      136
Exterior differential system      171 173
Extremal      275
Face      127 138
Field of hyperplanes      191
Fierz identity      15
First fundamental form      238
First integral      220
Flow of a vector field      219
Foliation      192
Foliation of Poisson manifolds by symplectic leaves      191
Fredholm      49
Front face      132
Full pair      213
Fundamental bundle      121
G-module      167
G-module with zero operators      169
Galileo group      96
Galileo transformation      97
Gamma matrices      135
Gamma matrices for C(n,m)      7
Gamma matrices of O(n,m)      7
Gauge covariant derivative      248 293
Gauge group      349
Gauge transformation      305
Gauss map      326 330
Gauss — Bonnet theorem      330
Gauss — Bonnet — Chem — Avez theorem      321 330
Gaussian curvature      321
Gaussian Integrals      57 61
Generalized first integral      220
Geodesics      275 279
Geometric simplex      127
Ghost field operator      370
Ghosts      363
Global function group      211
Goldstone bosons      320
Graded      124
Graded affine bundles      122
Graded algebra      1
Graded bundles      118 122
Graded chart      121
Graded commutative      1
Graded connections      125
Graded function      121
Graded manifold      121
Graded matrix      3
Graded spinor fields      125
Graded tangent      124
Graded tensor product      6
Graded vector bundles      122
Grading of a Clifford algebra      12
Grassmann algebra      119
Grassmann manifolds      108 109
Half-spinor representation      29
Hamiltonian function      184
Hamiltonian vector fields      164 184 186 188 212
Hamiltonian vector fields and automorphisms of a Poisson manifold      190
Hardy — Littlewood — Sobolev inequality      391
Harmonic      276 277 285
Harmonic gauges      275
Harmonic maps      274 281 406
Harmonicity conditions      405
Heat equation      175
Heisenberg group      163—165
Helicity      27
Helicity operator      27 32
Hermitian metric      299
Hermitian scalar product      299
Higgs mechanism      310 316
Higgs operators      244
Hodge theorem      321
Holonomy group      301
Homogeneous cochain      160
Homogeneous spaces      103 104 263
Homogeneous symplectic spaces      218
Homology      321
Homology group      129
Homomorphism central      141
Homomorphisms of a Lie algebra      102
Homothetic space-time      262
Homotopic      41
Homotopy class      275
Homotopy groups      41 43
Homotopy of topological groups      46
Hopf fibering      307
Hyperbolic metric      87
Hyperdifferentiable      52
Ideal      14
Indecomposable      112
Index of a Fredholm operator      49
Index of a vector field      322
Inequivalent spin structures      150
Infinite dimensional Lie algebras      364
Infinitesimal invariance      70
Injectivity radius of a riemannian manifold      429
Integral manifold      171
Integral manifold of a field of hyperplanes      192
Invariance group      175
Invariance of the equation of motion      79
Invariant connection      270
Invariant geometries on the squashed seven spheres      263
Invariant lagrangian      71
Invariant metric      288
Invariant polynomial      343
Involutive automorphism      103
Isogroup      175
Isotropy group of      106
Jacobi manifold      218
Jacobi operator      79
Jacobi structure      194
K-graded tangent bundle      122
Kac — Moody algebras      177 232 357
Kadomtsev — Petviashvili equation      232
Kaehlarian manifolds      235 294 299
Kaehler form      299
Kaehler metric      299
Kaluza — Klein theories      286
Killing vector fields      239
Kirillov local Lie algebras      193
Kirillov orbits      194
Kirillov — Kostant — Souriau theorem      218
Kondrakov Theorem      383 384 431
Kostant graded bundle      118 119 122
Lagrangian for a free Dirac particle      80
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