|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications |
|
|
|
| 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,  163 165
Pulse,  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  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,  426
Representations,  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  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
|
|
|
| Реклама |
|
|
|
|
|
О проекте