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| Miller W. — Symmetry Groups and Their Applications |
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| Предметный указатель |
Addition theorems 203 231
Adjoint group 182 183
Adjoint Lie algebra 183
Adjoint operator 92 414
Ado’s theorem 170
Ahlfors, U. 156 157 415
Analytic curve 165 166
Analytic manifold 165
Angular momentum operators 239 254
Angular momentum operators, orbital 269
Angular momentum operators, spin 269
Angular momentum operators, total 269
Annihilation operator 369
Anticommutation relations 369
Apostol 7 163 415
Associative algebra 132
Associative law 1 163
Automorphism group 8
Automorphism group of groups 6
Automorphism group of Lie algebras 170
Automorphism group, inner 8 182
Automorphism group, local analytic 170
Average 212
Axis of rotation 18
Balmer series 377
Bargmann, V. 263 4023 415
Baryon 268 37 3
Basis 17
Basis, canonical 257 298
Basis, orthonormal 18 66 412
Bessel functions 406 421
Biedenharn, L. C 415
Billings, A 415
Bisymmetric transformations 131
Boerner, H. 117 119 135 151 362 368 375 396 415
Boson 369 378
Bounded below (rep) 235
Bounded operator 413
Bounded set 21
Bounded set, branch 322 341 345 353
Branching laws 375
Burckhardt, J. 57 59 415
Campbell — Baker — Hausdorff formula 161
Campbell, L. 204 415
Canonical coordinates 178
Cartan’s criterion 392
Cascade particle 372
Casimir operator 234 260 394
Cauchy sequence 153 210 409
Cayley’s Theorem 12
Cell, primitive 37
Center (Lie algebra) 183
Centroid 25
CHARACTER 74 217
Character, compound 75 217
Character, simple 75 217
Character, table 85
Charge 372
Chevalley, C. 23 6 415
Circle group 215
Clebsch — Gordan coefficients 81 236
Clifford algebra 363
Closed set 211
Closed subspace 219 410
Cohen, A. 195 415
Cohn, P. 416
Commutator bracket 159 167 169 191
Commutator subgroup 205
Compact group 206 21
Compact set 211
Complementary series 304
Complexification (Lie algebra) 228
Congruent sets 20
Conjugacy class 5
Conjugate reps 389
Conjugate reps, self 389
Continuous function 206
Convergent sequence 409
Convergent Series 412
Convolution product 72
Cornwell, J. 416
Cosct 4
Cotton, F. 416
Courant, R. 416
Coxeter, H 416
Creation operator 369
Cross product 102 376
Crystal 52
Crystal, classes 53
Crystal, ideal 53
Crystal, real 53
Crystal, system 40
Crystallography point group 38
Crystallography restriction 39
Ctebsch — Gordan series 81 233
cube 31 90
Cullen, C 351 416
Curtis, C. 151 416
Cycle notation 3 137
Davydov, A. 416
De Vries, H. 165 368 391 416
Degeneracy 110 114
Degeneracy, accidcntal 110 114
Derived algebra 205
Determinant 2 19
Dettman, J. 416
Dihedral groups 29
Dirac equation 320 365
Dirac matrices 362
Dircct sum (reps) 68 79
Direct product 13 216
Direct sum (Hilbert spaces) 413
dodecahedron 32
Domain (of homomorphism) 7
Dynamical symmetry group 400
Dyson, F. 375 416
Eigenvalue 18 70 109
Eightfold way 373
Eisenhart, L. 416
Elastic interaction 266
Electron 268 319 362
Electron, shell 381
Energy, total 310 317
Equivalence classes 5 52 71
Erdelyi, A. 399 404 416
Euclidean algorithm 28
Euclidean group 20 190 278
Euclidean space 16
Euler angles 225 231
Event 293
Exponential mapping 175 177
Exponential matrix 152
Fermion 369 378
Finkbciner, D. 173 416
Fourier coefficients 412
Fourier series 215
Fourier transform 280
Frame Young 120
Frame Young, conjugate 389
Frame Young, inertial 293
Freudenthal, H. 165 368 39
Freudenthal, H.L. 416
Frobenius reciprocity theorem 84
Fundamental domain 37
Gamma function 204 246 422
Gaussian units 283
Gegenbauer polynomials 245
Gel'fand, I. 282 308 320 377 416
Gell — Man, M. 373 416
General linear group 2 128 321
| Generating function 203
Glide reflection 22
groups 1
Groups, abelian (commutative) 1
Groups, algebra (ring) 64 120 214 387
Groups, character 74
Groups, classical 171
Groups, conjugate 25
Groups, covering 225 290
Groups, crystal 53
Groups, cyclic 6
Groups, discrete 24
Groups, factor 5
Groups, isomorphic 6 25
Groups, lattice 34
Groups, Lie 162
Groups, nonsymmorphic 57
Groups, space 53 55
Groups, symmorphic 56
Guggenheimer, H 416
Hall, M 114
Hamermesh, M.L. 34 60 114 120 151 263 272 375 384 386 390 391 416
Hamiltonian operator 108
harmonic oscillator 10 397
Harmonic oscillator, group 397 400 403
Hausner, M 165 181 187 391 417
Heine — Borel theorem 211
Heine, V. 417
Helgason, S. 165 255 396 417
Helmholtz equation 64
Helwig, G 108 216 255 376 398
Helwig, G, 4 0 417
Henry, N. 417
Hermite polynomials 399 422
Hermitian matrix 173
Herzberg, G. 417
Hexagon 15
Hilberi, D. 416
Hilbert space 107 214 409
Hilbert space, separable 41
Holohedry 39
Holohedry, cubic 44 51
Holohedry, group 6
Holohedry, hexagonal 47 51
Holohedry, Homomorphism analytic 186
Holohedry, Lie algebra 170 178
Holohedry, local analytic 170 178
Holohedry, monoclinic 5 5 51
Holohedry, orthorhombic 49 51
Holohedry, rhombohedral 48 51
Holohedry, tetragonal 47 51
Holohedry, triclinic 50 51
Hydrogen atom 376
Hypercharge 372
Hypergeometcic functions 203 222 422
Icosahedral group 32
Ideal left 99
Ideal left, Lie algebra 185
Ideal left, minimal 99 100
Ideal left, right 99
Ideal left, two-sided 99
Idempotent 97
Idempotent, essential 120
Idempotent, generating 139
Idempotent, primitive 98
Identity element group 1 163
Identity element group, matrix 3 17
Identity element group, operator 17 20
Implicit function theorem 163 164
Ince, E 176 417
Indecomposable vector 79 129
Index {subgroup) 4
Infinitesimal operator 186
Inner (scalar) product 16 66 407
Inner (scalar) product, space (pre — Hilbert space) 66 407
Integrability conditions 195
Integrability conditions, function 205
Integrability conditions, invariant equations 278 294 313
Integrability conditions, measure 206
Integrability conditions, normalized measure 212
Integrability conditions, subset 9
Integrability conditions, subspace 67
Inverse, function theorem 63 177
Inverse, group 1 163
Inverse, matrix 17
Inverse, operator 17
Inversion operator 17 26 288
Inversion operator, space 288
Inversion operator, time 288
Inversion operator, total 288
Isobaric spin space 370
Isometry 20
Isomorphism group 6 182
Isomorphism group, inverted 142
Isomorphism group, Lie algebra 170 178
Isomorphism group, local analytic 170 178
Isomorphism group, pre — Hilbert space 409
Jacobi equality 168 169
Jacobi polynomial 257
Jacobian 163 165 177 206
Jacobson, N. 170 1
Jacobson, N., S 205 391 417
Jauch. J. 312
Judd, B. 417
Kamimura, H. 419
Kato. T 108 111 417
Kernel of homomorphism 7
Killing form 394
Klein — Gordon equation 317 362
KOREVAAR, J. 407 410 417
Kronecker della 3 17 423
Kursnnoglu, B. 377 417
Ladder (weight) 324 342
Ladder length 324
Lagrange's theorem 5
Laguerre polynomial 246 423
Lancaster, P. 349 417
Landau, L. 265 312 320 417
Laplace equation 242 249
Lattice 37
Lattice, base-centered 49 50
Lattice, body-centered 46 47 49
Lattice, Bravais 42 51
Lattice, crystal 37
Lattice, face-centered 46 50
Lattice, postulate 53
Lattice, primitive 47 48 49
Lattice, type 43
Lebedev, N. 259 417
Lebesgue integral 214 411
Legendre equation 238
Legendre function 231 241 423
Legendre polynomial 231 237 244 423
Lie algebra 168
Lie algebra, abstract 168 181
Lie algebra, commutative (abelian) 182
Lie algebra, compact 394
Lie algebra, complexified 184 228
Lie algebra, exceptional 392
Lie algebra, rank 395
Lie algebra, semisimple 391
Lie algebra, simple 392
Lie algebra, solvable 391
Lie algebra, subalgebra 184
Lie derivatives 189
Lie derivatives, equal 193
Lie derivatives, generalized 196 198
Lie derivatives, linearly dependent 193
Lie derivatives, linearly independent 193
Lie groups 162 165
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