|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications |
|
|
|
| Предметный указатель |
Doubly connected 110 334
Dual 262
Dual root forms 264
Duodecahedron 313
Dyadic 125
Dynamical group 460
Dynamical properties 145
Dynkin diagrams 278 298—316 307 318 321 324—326 422
Dynkin diagrams, connected 308
Dynkin diagrams, disconnected 308
Dynkin diagrams, double line 309 310
Dynkin diagrams, properties of 308—315
Dynkin diagrams, shrunk 310
Dynkin diagrams, simple chain 309
Dynkin diagrams, simple observations 307—308
Dynkin diagrams, split end 310
Dynkin diagrams, table of 324
Dynkin diagrams, triple line 309
Dynkin, E.B. ix 277 298 317
Dyson, F.J. 215
E series 286 288—292 310—312 314
E(2) 443 445 460 478
E(n) 451
Earth 438
Eckart, C. 277
Effective 367
Eigenavlue 248 254 265 318 352 354 355 363—365 369 430 497
Eigenoperator 279
Eigenoperator decomposition 138
Eigenspace 243 265
Eigenspace decomposition 422
Eigenstate 119
Eigenvalue decomposition 319 337 344
Eigenvector 229—234 242 244—246 248 263—265
Einstein relativistic velocity addition law 214 503
electromagnetic field 162
Electron 120 146 147
Electron wave function 53
Element of volume 391
Elliott, J.P. 349
Embedding groups 192—199
Empty set 57
Energy 424 425
Energy levels, statistical theory of 214
Engel, F. 86 119
Ensemble, orthogonal 214
Ensemble, symplectic 214
Ensemble, unitary 214
Equation of motion 159 160 167 168
Equator 389 390
EQUIVALENCE 18
Ergodic theorem 498
Euclidean group 83 443
Euclidean solids 313
Euclidean space 14
Euclidean volume element 79 80 391
Euclidean volume, of  398
Euler angles 180
Exceptional algebras 286 312 314
Exceptional groups 345 347 348
Excited state 158 163 164 175
EXP 15 16 22 23 110 126 144 149 158 201 202 204—208 214 222 249 274 317 350—354 358 363 365 387 401 440—442 444 454 461 462
Expansion of functions 33—37
Expansion of groups 212 213 436 477—492
expectation value 163 171 496—498
Exponential mapping 16 19 94 112 113 118 122 123 125 127 217 328—330 334
Factor algebra 225 256—258 305
Factor group 74 75 86 87 108 142 225 321 323—326
Factor group, discrete 84
Factor space 244
Factorial 2 140
Faithful 7 14 18 70 216 219 239 240 271 273 323 331 333 334 346
Faithful matrix representation 15 104 465 473
Faithful representation 113 253 280 293 302 304 321 322
Faithful representation of SU(2) 149
Fedenko, A.S. 435
Fermi — Dirac counting problem 32 33
Fermi — Dirac statistics 146
Fermion 499—501
Feynman, R.P. 56
Field 3 5 7 8 10 12 18 19
Field extension 241
Field inhomogeneity 176
Field, commutative 3 17
Field, complex 3
Field, noncommutative 17
Field, quaternion 3
Field, real 3
Field, representations for 16
Fine structure constant 349
Finite displacement 89—91 94
Finite group 2 55 83 118
First chain condition 264
First criterion of solvability 216 243—244 254
Flat geodesic submanifold 362
Flow process 66
Focal point 133 179 431
Fock representation 146
Fock, V. 435
Foldy — Wouthuysen transformation 430
Form factor 43
Forward light cone 377 378 380
Fractional linear transformation 372
Frame of reference 502—503
Franzini, P. 349
Freely falling coordinate system 41
Full reducibility 273
Fully reducible 236
Fully symmetric subspace 30—32
Fully, antisymmetric subspace 30—33 34 37
Function space 6 21 118
Function, Beta 400
Function, Gamma 140 400
Functional independence 237—241 263 264 274 276 280
Fundamental domain 328—330
G(3) 457
G(3, 1) 460
G(n) 457
G(p, q) 452 457
g* 201
Galilean algebra 220 221 505
Galilean group 243 452 456—459 472
Galilean group, Cartan — Killing metric 258
Galilean group, commutation relations 220 224 225
Galilean group, generators 219 457
Galilean group, regular representation 220 221
Gamma function 140 393
Gegenbauer polynomials 54
Gel’fand — Tsetlein patterns 402
Gel’fand, I.M. 23 56 277 435
General linear groups 24 25 26 53
General relativity 41
General shift 11 21
Generalized Inoenue — Wigner contraction 459
Generating function 149 157 172—175 179 180 181 382
Generating function,  140
Generating function, antinormal order 173 174
Generating function, Bessel functions 495
Generating function, harmonic oscillator eigenfunctions 496
Generating function, normal order 174
Generating function, spherical harmonics 495
Generating function, symmetrized order 174 175
Generators 13 89 100 103 332
Generators for 138 139 253
Generators for Galilean group 219 220 457
Generators for group 11
Generators for matrix group 93
Generators for orthogonal group 187 189 296 297
Generators for permutation group 189
Generators for symplectic group 188 189 296 297
| Generators for unitary group 186 189
Generators of infinitesimal displacements 89 275
Generators, compact 185 186 200
Generators, noncompact 185 186 200
Geodesic 127—129 131—133 179 362 383—391 431
Geodesic coordinates 385
Geodesic displacement 439 441 444 445
Geodesic orbit 386
Geodesic, broken 119
Geometric space 65 84 87 91 381 382
Gilmore, R. 181 215 277 435 506
Gl(1, q) 121 122 142—144 178 179
GL(2) 460 462 463
Gl(n) 481
Gl(n, c) 25 43 48 50 183—185 190 352 413
Gl(n, f) 86
GL(n, q) 25 43 48 50 51
GL(n, R) 2 25 43 48 50 183 184 190 197 199 352
Global Properties 78
Global properties of continuous group 75 76
Global properties of cosets 366—380
Global topological group 76
Globally isomorphic 110
Globally symmetric space 422
Good, R.H.Jr. 506
Gramm — Schmidt orthonormalization procedure 54
Great circle 444
Green’s function 349
Ground state 158 163 164 168—170 175—177
Group 1 10 15 19 20 320
Group elements 319
Group generators 95
Group integration 79—84
Group manifold 78
Group multiplication 1 94 113
Group multiplication in a continuous group 75 76
Group multiplication in contracted groups 493
Group of collinear transformations 66—71
Group of isometries 433
Group, abelian 3 95
Group, axioms 1
Group, bases for 11
Group, commutative 3 95
Group, composition function 103 107
Group, contraction 212 213 436—477
Group, derived 225
Group, direct product 142
Group, expansion 212 213 477—492
Group, factor 87
Group, finite 2
Group, generators for 11
Group, homotopy 129 130
Group, irreducible 236
Group, nilpotent 83
Group, noncommutative 4
Group, orthogonal 182 186—187 191 212
Group, representations 149 153 158
Group, simple 236
Group, solvable 225
Group, symplectic 182 187—189 212
Group, unitary 182 183—186 190 212
gyromagnetic ratio 162
H (field) 18
Haar measure 81 86
Haar measure on a coset 392
Hamermesh, M. vii 86 119 181 317
Hamiltonian 158 167 168 170 171 176 423—425 427—430
Hamiltonian for magnetic interaction 162
Han, M.Y. 435 506
Hansen, W.W. 181
Harish-Chandra 435
Harmonic oscillator algebra vi vii 349 423 461 496 498
Hausdorff space 59 61
Hausdorff, F. 94 119
Helgason, S. 86 215 435 506
Hermite polynomials 54 496
Hermitian antisymplectic matrix 346 347 366
Hermitian matrix 16 22 185 187 350—352 363 365 369
Hermitian matrix representative v
Hermitian symmetric matrix 347
Hermitian symmetric space 348 378 484
Hermiticity 180
Higher order iterations 116
Highest root 316
Hilbert space 147
Hilbert’s Fifth Problem 77
Hochstadt, H. 23 56
Holman, W.J. 277 317
Homogeneous coordinates 373 379—381
Homogeneous Lorentz group 85 395 401 502
Homogeneous polynomial 70 483 486
Homogeneous space 431
Homomorphic image 110 135 142 178
Homomorphism 14 18
Homomorphism among classical groups 52
Homomorphism,  128 129
Homotopy group 129—131 133 144 179
Homotopy group of SO(3) 130
Hydrogen atom 349 427—430
Hydrogen atom, bound states 428
Hydrogen atom, scattering states 428
Hyperbolic cotangent law 498
Hyperboloid 202—205 209 371 378—380 444 445
Hyperboloid, single sheeted 211 212
Hyperboloid, two-sheeted 85
Hypercharge 145 146
Hyperplane 300 302
i 3 17 18
icosahedron 313
Identities, trigonometric 15
Identity 1 3 5 8 9 68 69 107 320
Identity in continuous group 64
Identity in continuous group of transformations 65
Identity in group 23
Identity in vector space 23
Identity matrix 9 23
Image 60
Implicit function theorem 36
Improper subgroup 420
Indefinite metric 407
INDEX 253 319 353—354 422
Indicial condition 268
Induced metric 138
Induced transformation 138
Infinite sequence 328 330
Infinitely connected 334
Infinitesimal displacements 80 81 90 94 97 118 382—384 390 432 433 442 457
Infinitesimal displacements on plane 442
Infinitesimal displacements on sphere 442
Infinitesimal displacements, generators of 89
Infinitesimal generators 87—96 103 107 118 331 381 382
Infinitesimal generators, differential forms 213
Infinitesimal generators, Gl(1, q) 121—122
Infinitesimal generators, matrix groups 92—94
Infinitesimal generators, Sl(1, q) 121—122
Infinitesimal generators, SO(3, r) 124
Infinitesimal generators, SU(2, c) 123
Infinitesimal generators, U(2, c) 123
Infinitesimal length 390
Infinitesimal transformations 380—384
Inhomogeneous coordinates 373 379 380
Inhomogeneous group 451—453 455 457 493
Inhomogeneous Lorentz group 83 453 see
Initial conditions 100 103 112 160 161
Initial values 100 103
Injective 18
Inner automorphism 320 324 333
Inner product 42 43 319 323—325 327 331 332 337 353 354
Inner product in arbitrary representation 252 253
Inner product of Bloch states 171
|
|
|
| Реклама |
|
|
|
|
|
О проекте