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Choquet-Bruhat Y., Dewitt-Morette C. — Analysis, manifolds and physics
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Название: Analysis, manifolds and physicsАвторы: Choquet-Bruhat Y., Dewitt-Morette C. 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2Год издания: 1982Количество страниц: 630Добавлена в каталог: 12.01.2014Операции: Положить на полку |
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Cylindrical measures 573 576 Cylindrical subset 576 Darboux theorem 281 De Rham cohomology 223 de Rham complex 399 de Rham theorem 226 Decomposition theorem 399 Degenerate 285 Degree 556 557 Degree of a compact perturbation of Id 564 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 a tensor 139 Degree of an antiderivation 206 Dense 13 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 equation 416 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 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 202 269 317 Domain 2 Domain of dependence 515 Domain of integration 217 Dual 10 Dual, algebraic 10 Dual, star 295 Dual, topological 22 Duality 226 Dynamical systems 144 Effectively 153 Egorov theorem 40 Eigenvalue 60 Eigenvector 60 Eikonal equation 535 Einstein equation 342 356 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 224 395 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 163 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 Fixed point theorems 557 562 565 Flat connection 373 407 Flat space 299 622 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' 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 Fundamental vector field 360 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 curvature 396 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 grad 202 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, 172 Group, 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 39 180 189 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 Harmonic p-form 399 Hausdorff topological space 13 Heat diffusion 496 Heaviside function 447 Heine — Borel theorem 16 Hermitian metric 334 hessian 80 571
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