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Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications
Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications



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Название: Lie Groups, Lie Algebras and Some of Their Applications

Автор: Gilmore R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 587

Добавлена в каталог: 30.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Nonlinear transformation      372 436
Nonlocal metric      43
Nonorthogonal      171
Nonrelativistic limit      457 503
Nonsemisimple      233 236 255—258 261 273
Nonsemisimple algebra      279 436 449 463 471 472 477 492
Nonsingular      259 262 323
Nonsingular change of basis      91
Nonsingular matrix      2 23 97 375
Nonsingular metric      41 256 258 260
Nonsingular transformation      436 446 447
Nonsymmetric field, Einstein theory of      38
Nonsymmetry group      vi
Noonan, T.W.      56
Normal coordinates      498
Normal operator product      149
Normal order      172 173
Normal real form      257 334—337 339 340 347 407
Normal subgroup      72
Normalization, of root space diagram      281 292
Normalized measure      396—398
North pole      133 163—165 169 367 368 384—386 388 389 391 400 430 439—442 450 451
Notation, Dirac      55—56
Null space      464
Number operator      423 461
O(3, 1; r)      85
O(3, r)      85 86
O(n, c)      45—52 199
O(n, q)      45—52
O(n, r)      45—52 85 199
Oberhettinger, F.      23
octahedron      313
Off diagonal      195 346
Ogievetskii, V.I.      435
One parameter subgroup      94 111—113 328—330
One-dimensional abelian subgroup      113
Onto      18 319 320
Open set      59
Operator products, antinormal order      149
Operator products, normal order      149
Operator products, symmetrized order      149
Operator realization      19
Orbit      367 400 430
Orbital angular momentum      23
Order, antinormal      172 173
Order, normal      172 173
Order, of a group      2
Order, symmetrized      172 173
Ordered crystal lattice      498
Ordered operator products      149 172
Ordering operator      114—117
Ordering, of roots      299 301—302
Orthogonal algebra      186 191
Orthogonal complementary subspace      194 259 318 319 337 338 358 422
Orthogonal coordinate system      432
Orthogonal ensemble      214
Orthogonal functions      54
Orthogonal groups      45 182 186—187 191 294—297
Orthogonal groups, expansion of      479—481
Orthogonal matrix      19 352
Orthogonal polynomials      54
Orthogonal polynomials, Gegenbauer      54
Orthogonal polynomials, Hermite      54
Orthogonal polynomials, Jacobi      54
Orthogonal polynomials, Laguerre      54
Orthogonal polynomials, Legendre      54
Orthogonal polynomials, Tchebicheff      54
Orthogonal symmetry      188
Orthogonal, subspace      200
Orthogonality and completeness relations for Bessel functions      495
Orthogonality for harmonic oscillator eigenfunctions      496
Orthogonality for harmonic oscillator eigenfunctions for spherical harmonics      495
Orthogonality properties      374
Orthogonality relations      55 330
Orthogonality relations, contracted limit of      495
Orthonormal      54
Outer automorphism      320 324
Overcomplete      171
P*      201 202
P-representation      426
Packard, M.      181
Parallel displacement      132
Parallelopiped      404 405
Parameter space      126—128 328
Parameter space, contracted      126 127 444 450
Parameter sphere      129 130
Parameter, domain      365
Parameterization      94
Partial differential equations      103
Partial differential equations, decoupled      99
Particle at rest      395
Passive interpretation of transformation      66
Pauli spin matrices      17 123 275
Pauli, W.      181 435
Penguin      440
Perfect cosmological principle      431
Periodic      328 329
Permutation group      2 11 105 118
permutations      2
Philips, T.O.      349
Photon      53 149
Physical observable      v
Plane      209 210 213 445
Poincare group      83 453 456 493
Pointwise addition      21
Pointwise multiplication      21
Polar bear      440
Polarization      167
Pole, north      133 163—165 169 367 368 384—386 388 389 391 400 430 439—442 450 451
Pole, south      133 169 389
Polubarinov, I.V.      435
Polydisc      377 398
Polynomial      237
Polynomial bases      54
Polynomial, minimal      243
Polynomial, secular      243
Pontrjagin, L.      86
Position operator      461 498
Positive definite      38 41 146 307
Positive real numbers      15
Positive root      298 299 300 303—306 316
Potential, spherically symmetric      427
Precession, Thomas      214
Preliminary theorems      229—231 232 233
Principle of equivalence      66
Projection      105
Projection operator      105 118
Projective coordinates      370 371 382 397
Projective group      70 119
Projective mapping      372
Projective realization      375
Projective representatives      372—380 381 382
Proper invariant subalgebra      236 252
Proper subgroup      420
Proper subset      57
Pseudo-Euclidean space      492
Pseudo-Riemannian space      431
Pseudo-Riemannian symmetric space      407 409
Pulse, $\pi$      163 165
Pulse, $\pi/2$      163 164 165
q      17 18
q-representation      426
Quadrupole moment operator      424 425
Quantum field theory      119
Quantum numbers      144 145
Quantum theory      43
Quaternion      4—7 12 22 55 121 122 131 196
Quaternion covering group      142 143
Quaternion field      3 4
Quaternion hyperbolic space      372
Quaternion multiplication      17
Quaternion projection space      371
Quaternion projective sphere      371 372
Quaternion, representation for      17
Quesne, C.      435
Quotient      73
R      17 18
r-index      276
Racah, G.      86 277 317
Radial coordinate      432
Radial spherical coordinate system      431—433
Radian      2
Radical      225 234 235 256 258 261
Radicati, L.      349
Radiofrequency      162 164—167 176 177
Raise indices      39
Rank      237—241 244 245 251 254 264 211—274 279—285 298 299 316 317 319 328 329 332 335 354—362 422
Rank of classical groups, of SO(2n + 1)      240
Rank of classical groups, of SO(2n)      240
Rank of classical groups, of SU(n)      239 240
Rank of classical groups, of U(n)      239 240
Rank of classical groups, of USp(2n)      240
Rank theorem      264
Rank-1 column      401
Rank-1 coset      371 372 384 390 394
Rank-1 coset decomposition      319
Rank-1 row      401
Rank-1 space      431
Rank-1 space, expansion of      483—492
Rank-2 root spaces      280—285 286 302
Rank-class duality      405 406
rational      328 329
Rational number      85
Real field      3
Real forms      186 212 257 293 318—435
Real forms, classical groups      197—199
Real forms, compact      257
Real forms, noncompact      257
Real hyperbolic space      372
Real numbers      2 4 6 7 12 17 18 55
Real numbers, automorphisms of      320
Real projective space      370 371
Real projective sphere      371 372
Real restriction      421
Reality conditions      150 151 153 154
Reality restrictions      271 293
Realization      13 14 16 19 20 23 69 70 95 103
Rearrangement property      78
Recurring point      133
Recursion relation      268 269
Reduced mass      428
Reducible      223 224 236 259 280 346
Reducible, fully      236
Reduction      217
Regular      246 247
Regular element      263
Regular representation      106 118 218—221 223 224 226—228 234—240 243—254 258—261 265 266 271 273 274 302 317 321 322 327 330—334 336 338 350 354 362
Regular representation for algebra      218
Regular representation for field      218
Regular representation for Galilean algebra      220
Regular representation for group      218
Regular representation for linear vector space      218
Regular representation for nonsemisimple algebra      234—236
Relations, completeness      55
Relations, orthogonality      55
Renormalization      332
Reparameterization, of Lie group      79—80
Representations      7 13 14 16 23 85 95 100 103 106 114 135 136 142 230 231 233 244 245 252 253 269 271 316 319 321—323
Representations and BCH formulas      149 158
Representations for $Q_N$      44 45
Representations for algebra      19 149 153 158
Representations for complex numbers      4
Representations for field      16
Representations for group      149 153 158
Representations for linear vector space      18
Representations for nilpotent algebra      228
Representations for quaternions      4 17
Representations for solvable algebra      228
Representations of Gl(n, q)      44
Representations of ISO(2)      494
Representations of SO(3)      141 494
Representations of SU(2)      135—141
Representations, $p^—$      426
Representations, $q^—$      426
Representations, adjoint      106 216
Representations, complete system of      477
Representations, direct product of      143
Representations, irreducible      236
Representations, regular      106 216
Representations, simple      236
Representations, unitary irreducible      120 121
Resonance      162 163 176
Restriction of a field to a subfield      49
Restriction of a group to a subgroup      44 45 47—49
Riemann — Christoffel symbol      132 434
Riemannian manifold      131 132
Riemannian space      407 408 411 444
Riemannian space, curvature of      445 446
Riemannian symmetric space      132 182 213 319 353 357 359 362 372 383 387
Riemannian symmetric space, real forms of      412—419
Right coset      73 201
Right half-plane      71 72
Right invariant density      80
Right invariant integral      84
Right invariant measure      79—81
Right translation      2 79—83 92
Rigid translation of $R_1$      9 134
Rigid translation of circle      134
RMS      175
Robertson — Walker metric      431—432
Robertson, H.P.      56 431 432
Roman, P.      506
Root components, contravariant      263 264 270
Root components, covariant      263 264 270
Root forms      245 264
Root mean square      175
Root space      270 273 278 280—286 293 296 299 302 304 306—315 316 317 318 350 360—362 420 422
Root space decomposition      261 262
Root space diagram      272 279—286 293 328
Root spaces, icosahedral      312
Root spaces, octrahedral      312
Root spaces, properties of      244—248
Root spaces, tetrahedral      312
Root subspace decomposition      273
Root vector      246 247
Roots      241—248 254 262—272 278 279—285 286—290 298—316
Roots of secular equation      216 241 242
Rosen, J.      506
Rotation, Wigner      214
Rotations      2
Row, of a matrix      12
Rozenfeld, B.A.      435
Rudin, W.      56
Runge — Lenz vector      429
S      23 275
Saddle point      208
Saletan contraction      447 463—477 492
Saletan contraction in Kupczynski basis      472—477
Saletan contraction, commutation relations      466 476—477
Saletan contraction, first contraction      463—469 476
Saletan contraction, further contractions      469—472 477
Saletan contraction, necessary and sufficient conditions      464—467 475—476
Saletan contraction, structure constants of      475—477
Saletan contraction, termination of      471—472
Saletan, E.J.      447 463 506
Sankaranarayanan, A.      506
Santilli, R.M.      506
Scalar multiplication      3 5 8 10 13 18 21
Scattering states, of hydrogen      428
Schroedinger equation, for harmonic oscillator      496
1 2 3 4 5 6 7
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