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Ma Z.-Q., Gu X.-Y. — Problems and Solutions in Group Theory for Physicists |
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Предметный указатель |
matrix 403
matrix group 403
Anti-commutator 319
Associative law 27
Basis 7
Basis, orthogonal 212
Basis, standard 211
Block weight diagram 282 285 289 292 298 303 309 336 345 348 355 378 386 394 412 445 448
Bravais lattices 174 180
Cartan criteria 270
Cartan matrix 272
Cartan subalgebra 271 376 435
Cartan — Weyl bases 271 318 439
CHARACTER 43
Character table 48
Character, graphic method 213
Chevalley bases 280 321 378 409 436 441
class 30 48 54 139 422 424
Class, mutually reciprocal 30
Class, self-reciprocal 30 54
Clebsch — Gordan coefficients 80 101 106 149 154 215 243
Clebsch — Gordan series 80 240 299
Composition functions 140
Coset 29
Coset, left 29
Coset, right 29
Crystal 173
Crystal lattice 173
Crystal lattice, basis vector 173
Crystal lattice, basis vector of the reciprocal 175
Crystal lattice, vector 173
Crystal system 178
Crystallographic point group 174
CYCLE 193
Cycle structure 194
Determinant 1
Dominant weight diagram 299 301 356
Double-vector form 175
Dynkin diagram 272
Eigenequation 1
Eigenvalue 1
Eigenvector 1
Element 27
Element, conjugate 30
Equivalent theorem 404
Euler angles 123 125 127
Filling parity 214
Fock condition 199 323
Frobenius theorem 67 239
Gelfand bases 337
Generator 27 269
Gliding plane 178
Gliding vector 177 178
Group 27
Group space 52 140 269
Group, 37
Group, 38
Group, 35
Group, 32
Group, 32
Group, 35
Group, 65 68 69
Group, 68
Group, 68
Group, 33
Group, 32
Group, 34
Group, 32
Group, 73 75 106 121 134
Group, 59 70 85 101
Group, 40 81
Group, abelian 27
Group, covering 117 140
Group, direct product 51 55
Group, homomorphism 33
Group, improper point 51
Group, proper point 51
Group, quaternion 35
Group, quotient 31
Group, SO(3) 115
Group, SO(n) 375
Group, Sp(2l, R) 433
Group, SU(2) 117
Group, SU(n) 317
Group, USp(2l) 434
Height 282
Homomorphism 121
Homomorphism, kernel of 33
Hook number 198
Hook rule 198 325 380 405 442
Horizontal operator 199
Ideal 205
Idempotent 205
Idempotent, equivalent 205
Idempotent, orthogonal 205
Idempotent, primitive 205
Identity 27
Infinitesimal element 141
International notation 178
Inverse 27
Irreducible tensor operator 146
Isomorphic 27
Jordan forms 18
Killing form 270 320
Lie algebra 270
Lie algebra, classical 272
Lie algebra, compact 270
Lie algebra, exceptional 272
Lie algebra, rank 271
Lie algebra, semisimple 270
Lie group 115 140 269
Lie group, compact 140 269
Lie group, order 269
| Lie group, semisimple 269
Lie group, simple 269
Lie product 270
Lie theorem 141 142
Littlewood — Richardson rule 239 326 356 364 370 402
Lorentz group 415
Lorentz group, homogeneous 418
Lorentz group, proper 418
Lowering operator 280
Matrix 2
Matrix, hermitian 2 5
Matrix, negative definite 2 270
Matrix, positive definite 2
Matrix, positive semi-definite 2
Matrix, Real orthogonal 2 5
Matrix, real symmetric 2 6
Matrix, unitary 2 5
Multiplication rule 27
Multiplication table 27
Multiplicity 49 53 67 77 80 97 280 282 289 299 304 308 313 355 356 451 454
Order 140
Order of the element 29
Order of the group 27
Pauli matrices 3 33
Period 29
Permutation 193
Permutation parity 194
Permutation, even 194
Permutation, horizontal 199
Permutation, odd 194
Permutation, vertical 199
Planar weight diagram 283 288 289 292 298 306 340 345 348 355 360 372
Projection operator 81
Raising operator 280
Rank 2 142 146 317 321 326 327 376 379 380 440 441
Rearrangement theorem 27
Reduced matrix entry 147 149
Regular application 214
Representation 43
Representation, adjoint 142 283
Representation, conjugate 43
Representation, equivalent 47
Representation, faithful 43
Representation, identical 43
Representation, induced 66 237
Representation, inner product 237
Representation, irreducible 48 123 211 279 440
Representation, outer product 238
Representation, real orthogonal 43
Representation, reduced 47
Representation, reducible 47
Representation, regular 52 81 85
Representation, subduced 66 130 237 362
Representation, unitary 43
Representation, unitary of infinite dimension 166
Root 271
Root chain 271
Root, positive 271
Root, simple 271 319 435
Rotation 45 115
Rotation, improper 51
Rotation, proper 51
Schur theorem 47 143 245 321
Screw axis 177
Secular equation 1
Serre relations 280
Similarity transformation 8
Space group 174 186
Space group, symmorphic 174
Spherical harmonic function 399
Spin-tensor 405
Spinor 405
Spinor operators 407
Spinor representation 404
Structure constants 141 269 319
Subgroup 29
Subgroup, cyclic 29
Subgroup, index 30
Subgroup, invariant 30
Subgroup, normal 30
Symmetric center 177
Symmetric operation 173
Symmetric plane 177
Symmetric straight line 177
Symmetry transformation 44
Symplectic group 433
Symplectic group, real 433
Symplectic group, unitary 434
Tabular method 212
Trace 1
Transformation Operators for a Scalar Function 43
Translation group 173
Transposition 194
Vertical operator 199
Weight 279
Weight, dominant 282 336
Weight, equivalent 280 281
Weight, fundamental dominant 281
Weight, highest 282 337 379 442
Weight, multiple 279
Weight, single 279
Weyl orbit 280
Weyl orbital size 280
Weyl reciprocity 323 377 440
Weyl reflection 280
Wigner — Eckart theorem 51 147
Young operator 323 377 440
Young pattern 198 211 323 379 441 442
Young pattern, associated 214
Young tableau 198
Young tableau, standard 198
Young tableau, standard tensor 324 337 362 441
Young tableau, tensor 323
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