Ma Z.-Q., Gu X.-Y. — Problems and Solutions in Group Theory for Physicists :: Электронная библиотека попечительского совета мехмата МГУ

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Ma Z.-Q., Gu X.-Y. — Problems and Solutions in Group Theory for Physicists

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Название: Problems and Solutions in Group Theory for Physicists

Авторы: Ma Z.-Q., Gu X.-Y.

Аннотация:

Ma and Gu, both affiliated with the Institute of High Energy Physics in China, explain fundamentals of group theory. A beginning chapter reviews linear algebra, and subsequent chapters cover the concepts of a group and its subsets, the theory of representations of a group, and three-dimensional rotation groups. The remainder of the book is devoted to properties of some important symmetry groups of physical systems. Numerous exercises and solutions are included. The book is aimed at graduate students in physics who are studying group theory and its application to physics. It is also suitable for graduate students in theoretical chemistry

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 464

Добавлена в каталог: 02.12.2009

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Предметный указатель

$\gamma_{a}$ matrix      403
$\Gamma_{N}$ 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, $C_{10}$       37
Group, $C_{2n}$       38
Group, $C_{4h}$       35
Group, $C_{4}$       32
Group, $C_{6}$       32
Group, $C_{8}$       35
Group, $C_{N}$       65 68 69
Group, $D_{2n+1}$       68
Group, $D_{2n}$       68
Group, $D_{4}$       33
Group, $D_{N}$       32
Group, $V_{2}$       34
Group, $V_{4}$       32
Group, $\mathbf{I}$       73 75 106 121 134
Group, $\mathbf{O}$       59 70 85 101
Group, $\mathbf{T}$       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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