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| Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications |
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| Предметный указатель |
Bloch, F. 181
Block diagonal 27 41 227 242 260 346
Block diagonal matrix 195 350
Block submatrix 485—487 493
Block submatrix, decomposition 369
Boehm, A. 506
Bogoliubov, N.N. 56
Boost 214 219 457 502 503
Born, M. 56
Bornzin, G.L. 349 435
Bose — Einstein statistics 146
Bose — Einstein, counting problem 32
Boson 499—501
Bound states, of hydrogen 428
Boundary 77
Boundary values 269
Bounded 330
Bounded domain 370—372 377 378 382 398
Bounded groups 46
Bounded matrix elements 46
Broken geodesic 389
Buck, R.C. 56
Bulge displacement operators 425
C (complex field) 17 18
c (velocity of light) 457 503
Campbell, J.E. 94 119
Canonical 7 12 14
Canonical antisymmetric metric 41 42
Canonical basis 12
Canonical commutation relations 216 261—269 270—273 278 279 280 426
Canonical composition function 111
Canonical coordinates 425—427
Canonical coset decomposition 401
Canonical diagonal form, for Cartan — Killing metric 256 257
Canonical diagonal metric 185
Canonical form for bilinear antisymmetric metric 41—42
Canonical form for bilinear symmetric metric 40—41
Canonical form for metric 40—42
Canonical form for sesquilinear symmetric metric 40—41
Canonical form, Jordan 218
Canonical mapping  94
Canonical momenta 425—427
Canonical parameterization, for SU(2) 149 150 153
Canonical positive definite metric 279
Carrier space 29
Cartan criterion 216 255—261 273
Cartan decomposition 317 338 341 343 350 352 483—486 487 488 492
Cartan subalgebra 246 247 263 264 268—270 276 279 301 358—362 424
Cartan — Killing form 346
Cartan — Killing inner product 484—485
Cartan — Killing metric 216 248—255 261 262 273 322 323 327 330 331 333 334 346 354 387—389 406 407 433 484—485
Cartan — Killing metric, positive definite on Cartan subalgebra 269
Cartan — Killing metric, properties of 250
Cartan, E. x 108 248 255 277 427 435
Casimir invariant 100 264 316 479—483 486 488 495
Casimir invariant for semisimple groups 483
Casimir operators 276 357 358 362 433
Causality 146
Cayley numbers 17 18
Chain condition, first 264—265
Chain condition, second 265—270
Chain rule 35 36
Chain, of roots 246 264 265 267—269 302
Chakrabarti, A. 506
Change of basis 24—26 52 217 436 460
Change of basis in topological space 79
Change of basis, induced 28 29
Change of basis, local 107
Change of basis, matrix transformation 53
CHARACTER 332 335 347—350
Character of real forms 257
Character of symmetric space 421—422
Characteristic size 439 478
Charge 146
Chevalley, C. 56 86
Churchill, R.V. 435
circle 6 328
circular polarization 162 167
Circumference of torus, major 71 72
Circumference of torus, minor 71 72
class 405 406
Classical algebras 182—215 293—298 316 348
Classical compact group 319
Classical cosets, properties of 363—406
Classical groups 24—56 85 182 401—406
Classical groups, canonical parameterization of 401—406
Classical groups, Lie algebra for 182
Classical matrix groups 45 66 84 110
Closed 60 85
Closed subgroup 73 320 330 333
Closed, algebraically 241
Closure (algebraic) 1 3 5 8 64 65 68 69 320
Closure (topological) 60
Coefficients of the connection 434
Cogredient 26
Coherent state 171 175
Cohn, P.M. 86 106 119
Coleman, A.J. 86
Collineation group 72 89—94 96 98—99 103—104 106 109 112 113
Column, of a matrix 12
Commutation relations 9 19 22 94—96 103 105 106 182 186 187 189 196 212 216 217 225 226 229 237 261 264 266—268 270—272 279 293 296 324 350
Commutation relations for  460
Commutation relations for  189
Commutation relations for E(n) 450 451
Commutation relations for G(n) 452 456
Commutation relations for G(p, q) 452
Commutation relations for Gl(1, q) 122
Commutation relations for ISO(2) 442
Commutation relations for ISO(n) 450 451
Commutation relations for ISO(p, q) 452
Commutation relations for IU(n) 481
Commutation relations for O(n) 187 189
Commutation relations for Sl(1, q) 122
Commutation relations for SO(3) 442
Commutation relations for SO(n) 450 458 472
Commutation relations for SO(n, 1) 451 452
Commutation relations for SO(p, q) 452
Commutation relations for Sp(2n) 189
Commutation relations for SU(2) 123
Commutation relations for SU(n) 186 189
Commutation relations for U(2) 123
Commutation relations for U(n) 186 189
Commutation relations, canonical 216 270 279
Commutative 3 224 317
Commutative field 3 51
Commutative group 3 95
Commutativity 3 5 17 18
Commutator 9 94 95 104 117 228 246 263 264 272 320 321 336
Commutator in a group 95 96 225
Commutator in Regular representation 221 223
Commute 339
Commute, group operations 108 109
Compact 46 60 85 110 113 127 258 327 330 333 336—339
Compact generators 185 186 195 200 412—419 421
Compact group 81—83 351
Compact real form 199 200 257 335—337 343 347 407 421
Compact subgroup 384
Compactness 16 60
Complement 60
Complementary subspace 200 319
Complete reducibility 259 261
Complete set 138 141 143 179
Completeness relation 55
Completeness relation, contracted limit of 495
Completeness, of simple root spaces 278 279 286 298 315
Complex conjugation 4 183 266 336 337 339 344
Complex extension 182—188 212 241 293 318 336 411 420 421
Complex field 3
Complex hyperbolic space 372
complex numbers 2 6 7 12 15—18 55
| Complex projective space 371
Complex projective sphere 371 372
Complex semisimple algebra 318 319
Complex variable 372
Composition function 77 107
Composition function for Lie group 94
Conformal group 349
Conformal mapping 372
conjugate 4 5
Conjugate groups 72
Conjugate subgroup 72 94
Conjugation 321
Conjugation, complex 4 183
Conjugation, quaternion 4
Connected 71 83 85 129
Connected component 71 72 74 75 77—79 84 323
Connected continuous group 84
Connected Dynkin diagram 317
Connected, multiply 134
Connected, simply 87 134
Connectivity 129 199—200
Conservation laws 145
Constitutive relations, for roots 280
Constraints, linear 403
Constraints, nonlinear 403
continuous 61
Continuous deformation 71 129 130
Continuous group 2 63 57—86
Continuous group of transformations 57 64 65 68 84
Contract (tensor) 56 249
Contracted algebra 436 492
Contracted group, multiplication law in 493
Contraction of groups 83 212 213 436—477 492
Contraction of tensors 56 249
Contraction, commutativity of 469—470
Contraction, first 463—469
Contraction, further 469—472
Contragredient 26
contravariance 25—26 52 56
Contravariant 26 28 31 34
Contravariant root 266 270
Convergence 60
Convergence point 133
Convergent subsequence 60
Converse to Lie's theorems, to first theorem 106—108
Converse to Lie's theorems, to second theorem 106—108
Converse to Lie's theorems, to third theorem 106—108 120
Coordinate patch 127
Coordinate system 7 20 62 88—90 97 439 442 443
coordinates 25 26 62 97 112
Coordinatized 84
Correlation function 171
Coset 73 74 132 200—213 350—406
Coset after Inoenue — Wigner contraction 493
Coset decomposition 182 201
Coset in Cartan decomposition 493
Coset, dimension of 347
Coset, left 201
Coset, rank 347
Coset, representative 74 75 86 168 182 222 223 319 321 363—406
Coset, right 201
Cosine 15 281
Countable 77 78
Counting problems, Bose — Einstein 32
Counting problems, Fermi — Dirac 32—33
Courtens, E. 181 506
Covariance 25 26 52 56
Covariant 26 28 31 34
Covering group 108 110 178 179
Coxeter, H.S.M. ix
Creation operators 423—425 427 461 499—501 505
Creation operators for Bosons 499—501 505
Creation operators for Fermions 499—501 505
Criterion of solvability, first 243—244
Criterion of solvability, second 253—254
Criterion, Cartan’s 255—261
Crittenden, R.J. 86
Cross contraction 249
cube 313
Cunningham, E. 349
Curvature of a group 444
Curvature of a Riemannian space 486—487
Curvature tensor 132
Cyclic abelian group 200
Cyclic group 179
de Saint-Exupery, A. 438 506
de-Sitter group 349 453
Defining matrix representation 453
Defining representation 239 240 331 332 339 340 346 351 354
Defining representation of a classical algebra 213
Definite metric 407
Definition, domain of 77
Degeneracy vi
Degenerate 250 253 348
Degree of freedom, in contraction 459
Dense 329
density 80
Density function 81
Derivation 8 10 105 322
Derivative 8 15 224
Derivative property of Lie bracket 423
Derivative, Lie 105
derived 224
Derived algebra 224 227 228 229 235 241 244 246 250 253 254 469 470
Derived group 225
Derived series 224
DET 37 50
Determinant 2 19 21 22 37 85 175 237 238 241 248—250
Diagonal 139 157 158 327 329 331 332 335 352 364
Diagonal matrix 22
Diagonal metric 40 43
Differentiable equation 100—101 112
Differentiable manifold 61
Differential form 275
Differential operator 357
DIMENSION 7 12 14 18 47—52 73 84 239 242 280 291 316 332 335 359—362
Dimension of linear vector space 7
Dimension of simple algebras 291 292
Dimensional analysis 269
Dimensionality, of classical groups 47—52
Diophantine equation 287 311 312 313
Dirac Hamiltonian 429 430
Dirac notation 55—56
Direct product 26 53 73
Direct product group 28 142
Direct product vector space 28
Direct sum 26 53 73 242 278 280 284 317
Direct sum algebra 142
Direct sum group 27
Direct sum vector space 27
Direction cosines 163—166 281 307 312 328 329
Disconnected Dynkin diagram 307
Discrete factor group 74 75 321
Discrete group 74 75 83 86
Discrete invariant subgroup 87 108—110 118 133 134 142 144 178—280 200 334
Discrete invariant subgroup of SU(2) 130
dispersion 176 177
Displacement 97 391
Displacement, finite 89—91
Displacement, infinitesimal 89
Distance 319
Distance on a coset 385—391
Distributive law 3
Division ring 18
Donut 71 72
Donut surface 85
Double-sheeted hyperboloid 407
Double-valued 146 179
Double-valued representations 120
Double-valued representations of SO(3) 149
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