Tung W.K. — Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions :: Электронная библиотека попечительского совета мехмата МГУ

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Tung W.K. — Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions

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Название: Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions

Автор: Tung W.K.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 344

Добавлена в каталог: 17.03.2008

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Предметный указатель

Orthogonal complement      33
Orthogonal group      16 283
Orthogonal group O(2)      214
Orthogonal group O(3)      222
Orthogonal matrix      82 177 283
Orthogonal operator      306
Orthogonality      303
Orthonormal basis      303
Orthonormality      303
Orthonormality and completeness of group characters      42
Orthonormality and completeness of representation functions of       8
Orthonormality and completeness of SO(2) representation functions      88
Orthonormality and completeness of SO(3) representation functions      133
Orthonormality of representation matrices      39
Orthonormality of spherical harmonics      146
Parity      149 217 223 226 227
Parity derived      227
Parity eigenstate      227
Parity intrinsic      227
Parity of permutations      65
Parity transformation      10 221 228
Partial wave expansion      112 140
Partition      65
Passive transformation      3 263
Past cone      178
Pauli matrices      106 127 180
Pauli wave function      114
Pauli — Lubanski vector      195
Permutation group      16 64
Permutation horizontal      67
Permutation symmetry      10 64
Permutation vertical      67
Perturbation amplitude time-reversal invariance of      259
Peter — Weyl theorem      134
Phase convention      105 217 252
Phase relative      161 217 235
Phase shift      261
Plane wave basis      92 111 162 168 193 198
Plane wave expansion      147 206
Plane wave photon states      147
Plane wave solutions      206
Poincare group extended      231
Poincare group full      246
Poincare group proper      181
Point groups      10
Polarization vector      148
Primitive idempotent      310
Principal series      191 330
PRODUCT      12
Product direct      direct product
Product group      12
Projection operator      57 299 303 309
Projection operator for the rotation group SO(2)      91
Projection operator for the rotation group SO(3)      135
Projection operator irreducible      57
Proper Lorentz group      177
Proper Lorentz group, irreducible representations of      187
Pseudo-scalar      224 230 288
Raising operator      103 157 284
Real general linear group      277
Realization of discrete translation group      6
Realization of group transformations      27
Realization of symmetry operations      3
Rearrangement Lemma      16 86 129
Recurrence relations      142
Recursion formulas of Bessel functions      163
Recursion formulas of spherical harmonics      145
Reduced matrix element      60
Reducible representation decomposition of      44
Reflection class of      214
Reflection operator      214 287 289
Regular representation      45—46 307
Relativistic field operators      203
Relativistic wave equations      202
Relativistic wave functions      202
Relativity special      173
Representation      5 27
Representation decomposable      33
Representation direct sum      36
Representation double-valued      106
Representation equivalence of      32
Representation faithful      27
Representation fully reducible      33
Representation irreducible      33
Representation matrix      28
Representation multi-valued      88
Representation of a group algebra      308
Representation of symmetry operations      3
Representation of the group       6
Representation reducible      33
Representation regular      45
Representation unitary      35
Right coset      21
Right multiplication      309
Ring      307
Rotation      10
Rotation as special case of Lorentz transformation      176
Rotation in three dimensions      94
Rotation in two dimentions      82
Rotational symmetry discrete      10
scalar      230 288
Scalar product      178 302 323
Schmidt orthonormalization procedure      304

Schur's lemma      37
Second quantized theory      116
Selection rules      123
Self-adjoint operators      305
Signature of a metric tensor      278 284
Signature of space-time metric      177
Similarity transformation      300
Simply connectedness of SL(2) group      180 282 320
Simply connectedness of SO(2) group      83 287
Simply connectedness of SO(3) group      94 288
Simply connectedness of SO(3, l) group      177 288
Simply connectedness of SU(2)      127
Space 2-dimensional space      212
Space 3-dimensional space      221
Space group      10
Space invariance      212
Space inversion 10      228
Space-like 4-vector      199
Space-time symmetry      10
Space-time symmetry, discrete      10
Special linear group      280
Special orthogonal group      286
Special orthogonal matrix      82
Special relativity      10 173
Special unitary group      16 283
Spherical Bessel function      171
Spherical harmonics      135 223
Spin intrinsic      136 195
Spinors      320
Spinors Dirac      326
Spinors with dotted index      324
Subgroup      15
Subgroup, one parameter      99
subspace      297
Symmetric group      16 64
Symmetric operator      306
Symmetrizer      65 67
Symmetrizer anti-      67
Symmetrizer irreducible      67
Symmetrizer Young      67 272
Symmetry      3
Symmetry class of tensors      73 272
Symmetry internal      11
Symmetry mirror      10
Symmetry permutation      10
Symmetry preserving operator      72
Symmetry rotational      80 94
Symmetry space-time      9 173 212
Symmetry transformation      3
Symmetry translational (discrete)      3
Tensor anti-symmetric second-rank      189
Tensor components      71
Tensor of symmetry $(\lambda, \mu)$       272
Tensor of symmetry $\Theta^{p}_{\lambda}$       73
Tensor of symmetry class $\lambda$       73
Tensor of type (1, 1)      266
Tensor of type (i, j)      270
Tensor of type (i,j; k, l)      276
Tensor space      71 270 276
Tensor symmetric second-rank      189
Tensor totally anti-symmetric      74 95 175 280
Tensor totally symmetric      74
Tensor traceless      270 285
Tensor with mixed symmetry      75
Three-cycle      17
Three-j symbols      121
Time reversal invariance      10 259
Trace of an operator      301
Traceless tensor      285
Transformation formula of creation and annihilation operators      206
Transformation formula of operator fields      117 203
Transformation formula of operators      114
Transformation formula of spherical harmonics      144
Transformation formula of wave functions      113 203
Translation in space      9 89 152 166 181
Translation in time      9 181
Translation on a lattice      3 10
TRANSPOSE      293
Two-cycle      17
Unitary group      16 277
Unitary group of signature ( , )      278
Unitary operator      3 305
Unitary representation      35
Vacuum state      147 206
Vector      292
Vector axial      231
Vector null      295
Vector space conjugate      265
Vector spherical harmonics      149
Vector with contravariant index      264
Vector with covariant index      264
Vector with dotted contravariant index      265
Vector with dotted covariant index      265
Velocity of light      173
Wave equation relativistic      202—203
Wave function relativistic      202
Wave function transformation properties of      113—114
Wave vector      7 148
Wigner — Eckart theorem      60
Young diagram      65
Young tableau      66 272
Young tableau, normal      66
Young tableau, standard      66

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