Carmeli M. — Classical Fields: General Gravity and Gauge Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Carmeli M. — Classical Fields: General Gravity and Gauge Theory

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Название: Classical Fields: General Gravity and Gauge Theory

Автор: Carmeli M.

Аннотация:

This textbook for a one-year graduate course in theoretical physics explores the classical theory of fields with a mix of electrodynamics, gauge fields, and gravitation. Carmell (Ben Gurion) develops the geometry of curved spacetime, the Einstein field equations, gravitational fields of elementary mass systems, the equations of motion in general relativity, spinor formulation of gravitation and gauge fields, and the gauge theory of gravitation.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 650

Добавлена в каталог: 09.06.2006

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Предметный указатель

"Tail" (of radiation)      201 203 255
$D^{(m/2,n/2)}$ (spinor representation)      411
$D^{(m/2,n/2)}$ (spinor representation), particular cases of      413 415
$O(4)\times SU(2)$ (group)      472
$SL(2,C)\times SU(2)$ (group)      593—595
$SL(2,C)\times U(1)$ (group)      555 580 586 587 590
$SL(2,C)\times U(1)\times U(1)$ (group)      590—593
$SU(2)\times SU(2)$ (group)      471—480
$SU(2)\times U(1)$ (group)      309 580
$\sigma^{\mu}_{AB^{'}}$ (matrices)      416 420 421 434
$\sigma^{\mu}_{ab^{'}}$ (null tetrad matrices      568 570 571 572—578 586 587
't Hooft, G.      578
Abelian gauge fields      559—560
Abelian gauge theory      560
Abelian group      560
Abelian solutions of Yang — Mills theory      600—601
Action functional      310
Action integral for gravitational field      93—105
Action principle      310—311
Action-at-a-distance      3 313
Adapted coordinate system      131 172
Advanced time      279
Affine connection      46 424 426 471 567
Affine connection, spinor      419 420 424 426 566 567
Affine connection, torsion-free      551
Affine parameter      64—65
Algebra of the matrices      472—476
Algebraically special solution      389 390
Anandan, J.      552
Angle of deflection of light      224
Angle of deflection of light, Newtonian calculation of      225—226
Angles Euler      445
Angular velocity      212 213
Anholonomic basis      556
Anticommutation relation      473
Antisymmetric tensor      26
Antisymmetrization      28
Aperiodic solution      200
Arecibo Ionospheric Observatory      229
Ash, M.E.      265
Asymptotic flatness      239 240
Atlas      555
atomic clocks      214
Auslander, L.      616
Axisymmetric solutions of Einstein field equations      365—406
Bardeen, J.M.      144
Base space      562
Bases      556
Basis spinor      445 446
Basis vectors      556
Basombrio, F.G.      616
Batygin, V.V.      264
Bazanski, S.      310 363
Beiglboeck, W.      627 628 630 630
Bel, L.      405
Bertotti, B.      281 363
Bessel equation      8 10
Bessel function      8 9 199
Bessel, F.W.      13 14
Bianchi identities      80—82 139—141 296 432—433 442 568 570 614
Bianchi identities for coupled gravitation and gauge fields      594
Bianchi identities for gauge fields      448
Bianchi identities, contracted      81—82 85 266
Bianchi identities, spin-coefficient form of      137
Bijection      555
Binary star      262
Birkhoff theorem      160
Bisurface      172 367
Bjorken, J.D.      19
Black hole      401 404 610
Boltzmann's constant      259
Bondi coordinates      244—246
Bondi news function      241
Bondi — Metzner — Sachs group      242
Bonnor, W.B.      281
Boost      457 458
Borel, A.      551
boundary conditions      400—401
Boyer, R.H.      405
Boyer-I indquist coordinates      383 387 396 400 402
Braginsky, V.B.      14 19
Brehme, R.W.      618—630
Bremsstrahlung, gravitational      255—265
Brocket man, R.A.      265
Bruhat, Y.      154
Bundle space      559 562
C-invariance      555
Campbell, D.B.      265
Canonical cylindrical coordinates      175 370 371 380
Canonical form      515—516
Canonical spheroidal coordinates      363
Carmeli, M.      19 135 154 204 230 259 260 265 280 331 336 363 389 404 405 514 517 543 551 552 554 562 570 607 612 616
Carmell classification scheme      509—516 530—532 533
Cartan, E.      408 480
Carter, B.      366 405
Cartesian coordinates      11 33 113 161 206 224 421 558
Cartesian coordinates, isotropic      162
Cartesian product bundle      559
Casimir operator      334 346 348 350 358
Castillejo, L.      552
Cauchy problem      152 153
Caustic surface      192
Center of mass      618 628
Centrifugal force      14—16
Change of basis for spinors      461 463
Charach, Ch.      331 336 363 480 543 616
Characterization of mass center      626—628
Chart      555
Chern classes      530—352
Chern polynomial      551
Chern, S.S.      551
Cho, Y.M.      552
Choice of coordinate system      244—246 270—271
Christoffel symbols      45—51 424 426 471
Christoffel symbols, transformation laws of      46—48
Classical fields      vii 267 310
Classical mechanics      1
Classification by spinor method      500—507
Classification of electromagnetic field      481—488 517—520
Classification of electromagnetic field, diagram of      485
Classification of gauge fields, diagram of      514
Classification of gauge fields, eigenspinor-eigenvalue equation of      509—516
Classification of gauge fields, four-way scheme of      532—552
Classification of gauge fields, Lorentz invariant versus gauge invariant methods      530—532
Classification of gauge fields, matrix method      517—529
Classification of gravitational and gauge fields      481—552
Classification of gravitational field      130 488—509
Classification of gravitational field, diagram of      503 505
Classification of gravitational field, eigenspinor-eigenvalue equation of      500—507
Classification of Weyl tensor      490—492
Classification of Weyl tensor, eigenvector-eigenvalue equation of      490
Classification, Carmeli      509—516 530—532 533
Classification, Penrose      492—507
Classification, Petrov      488—492 507 509
Classification, Wang — Yang      514 517—529 530—532 534
clocks      213 214
Collapse      198
Collapsed object      365
Collapsed rotating object      366
Collapsing matter      189
Collision      255
Combined gravitational and electromagnetic fields      586—590
Commutation coefficients      556
Commutator      68 421 446 556
Commutator equations      137
Commutator operator      421 429 433
Comoving coordinates      190—192
Compact group      445
Complete manifold      165
Complex conjugate bundle      563 564

Complex potential      388
Complex rotation      482 491
Complex vector bundle      559 562
Complexification isomorphism      561
components      22
components of vector      22
Components, irreducible      73
Conformal mapping      74
Conformal mapping of gauge fields      470
Conformal scale group      563
Conformal space      73
Conformal spinor      437 439—442 467
Conformal structure of spacetime      235—239
Conformal tensor      72—76 237 238 367 464
Conformal transformation      235 237 239 242
Conformal transformation, properties of      73—76
Conformally fiat space      172
Connected manifold      555
Connection      557 558
Conservation law of angular momentum      250
Conservation laws in presence of gravitation      247—248 250
Conservation of isospin      449—450
Conserved currents      599
Constant of motion      624
Constant-phase solution to Ernst equation      382
Contracted Bianchi identities      81—82
Contraction      25 417
Contravariant tensor      23
Contravariant vector      22 556
Coordinate basis      556
Coordinate conditions      151—152
Coordinate conditions, deDonder      152 281 296 300 301
Coordinate singularity      165
Coordinate system, Fermi      51 270 558
coordinates      20—22
Coordinates, adapted      131 172
Coordinates, Bondi      244—246
Coordinates, Boyer — Lindquist      383 387 396 400 402
Coordinates, canonical cylindrical      175 370 371 380
Coordinates, canonical spheroidal      383
Coordinates, Cartesian      11 33 113 161 206 224 421 558
Coordinates, choice of      244—246 270—271
Coordinates, comoving      190—912
Coordinates, curvilinear      12
Coordinates, cylindrical      7—10 175 370
Coordinates, ellipsoidal      177
Coordinates, Fermi      51 270 558
Coordinates, freely falling      11
Coordinates, geodesic      50 82 247 248
Coordinates, harmonic      152 281 296 300 301
Coordinates, inertial      1 2 12
Coordinates, isotropic Cartesian      162
Coordinates, isotropic spherical      162 230
Coordinates, Kerr      400 402
Coordinates, Kruskal      163—168
Coordinates, local      557
Coordinates, noninertial      11 12
Coordinates, null      183 337 459
Coordinates, prolate spheroidal      177 181 375 379
Coordinates, retarded time      337 343 389 390 391 459
Coordinates, rotating      12
Coordinates, spherical      381
Coordinates, spheroidal      377 389
Coordinates, transformation of      20—23 113 172 276
Corinaldesi — Papapetrou supplementary condition      326 331—334 338 360
Corinaldesi, E.      322 326 328 331 363
Coriolis force      212
Correspondence between spinors and tensors      416—419
Cosmological constant      87 240 467
Cotangent space      557
Coulomb collision      255
Coupling matter and gauge fields      569—571
Covariance group of Ernst equation      388—389
Covariant derivative      53 557 618
Covariant derivative of spinor      419—421
Covariant derivative operator      420 421 557
Covariant derivative, double      471 593—594
Covariant derivative, gauge      447—448
Covariant derivative, horizontal      620—623
Covariant derivative, vertical      620—623
Covariant differentiation      51—61 557 618
Covariant differentiation, rules for      55—58
Covariant tensor      23
Covariant vector space      556
Covariant vectors      23 557
Covering group      416 445
CPT-invariance      555
Crammer, J.      267 322 363
Cranshaw, T.F.      214 215
Cross section      495 562
Curl      141 373
Current vector      107 111 142 312
Curvature spinor      428—434
Curvature spinor, spinor equivalent of      434—435
Curvature spinor, symmetry of      430—431
Curvature tensor      67—80 237 428 429 431 432 434—435 464 465
Curvature tensor, symmetry of      70—71
Curvature, Gaussian      76
Curvature, mean      76
Curvature, scalar      238
Curve, null      66
Curved spacetime      13 20 415 416
Curved spacetime, geometry of      20—83
Curvilinear coordinates      12
Curzon metric      380
Curzon, H.E.J.      381
Cylindrical coordinates      7—10 175 370 380
Cylindrical gravitational waves      198—199 235
D'Alembertian operator      208 242 278
D(g) (operator)      409
Debever — Penrose equation      492
Debye shielding radius      259
Decomposition of Riemann tensor      78 434—435 443
Decoupled electromagnetic equations      147—148
Decoupled gravitational equations      144—147
DeDonder coordinate condition      152 281 296 300 301
Deflection of light in a gravitational field      222—226 234
Deformation parameter      384
Delay of radar pulses in gravitational field      227—230
Delay of radar pulses in gravitational field, angle of      224
Delta, covariant derivative of      56
Delta, Dirac      111 201
Delta, generalization of      31
Delta, Kronecker      22 26
Demianski — Newman metric      386—387
Demianski, M.      366 386 405
Densities, Levi-Civita      37—38 422 423
Densities, scalar      35
Densities, tensor      35—45
Densities, vector      35
Densities, weight of tensor      35
Derivative, covariant      51—61 557 618
Derivative, directional      186 392 555 571 602
Derivative, double covariant      471
Derivative, gauge covariant      447—448
Derivative, intrinsic      137 571
Derivative, Lie      113—122 622
Detection of gravitational waves      227
DeWitt, B.S.      618 630
Diagram of classification, of electromagnetic field      485
Diagram of classification, of gauge field      514
Diagram of classification, of gravitational field      503 505
Diagram, Kruskal      167
Diagram, Penrose      236 237 240 503 505
Dicke, R.H.      14 16 19 299
Differentiable manifold      555
Differential forms      161
Differential geometrical analysis      553—558
Differential geometry, an introduction      555—558
Differential geometry, an introduction, general relativistic interpretation of      558—559

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