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

Abelian group      13
Action transformation      3 263
Addition of linear transformations      298
Addition of vectors      295
Addition theorem      145 164
Adjoint operator for anti-linear operator on the dual vector space      302
Adjoint operator for anti-linear operator on vector space      304
Algebra of linear transformations      298
Alternating group      65
Angular momentum basis      160 170 220 226 238
Angular momentum basis orbital      138
Angular momentum basis spin      138
Annihilation operators      147 206
Anti-linear transformation      248 331
Anti-particle      205
Anti-symmetrizer      65
Anti-unitary operator      249 332
Anti-unitary operator, time-reversal as an      250
Associativity      12 295
Axial vector      231 287
Basis      296
Basis, canonical      105
Basis, vectors      292
Bessel function      158 163
Bessel function, spherical      171
Bispinors      327
Bispinors, symmetric      231
Bloch wave function      7
Boost Lorentz      176 228
Bose — Einstein system      134
Branching ratios      62 123
Casimir operator      103 157 191 195 224
Cayley's theorem      17
Center      24
CHARACTER      32
Character, for direct product representation      49
Character, for rotation group SO(3)      109
Character, table      43
Charge conjugation symmetry      205 212
Charge conservation      10
class      19
Class of permutations      20
Class of the rotation group SO(      3 97
Classical groups      16 80 262
Clebsch — Gordan coefficients      50 120
Commutation relations      Lie algebra 101
Commutativity      295
Commutator      101
Compactness of rotation group SO(3)      96
Compactness of SU(2)      127
Compactness of unitary groups      279
Complementary series      191 330
Completeness of irreducible representation matrices      8 41 47
Completeness of spherical harmonics      146
Condon — Shortley phase convention      105 120
Conjugate group elements      19
Conjugate subgroup      20
Conjugate vector space      265
Continuous groups      15 80 290
Contraction      265 266 270 323 325
Contractions by invariant tensor      282
Contractions by the metric tensor      284
Contravariant four-vector      177
Contravariant vector components      292 323
Contravariant vector with dotted index      265
Coordinate transformation      263
Coset      21 215
Covariant four-vector      178
Covariant normalization      201
Covariant vector components      264 292
Covariant vector with dotted index      265
Covering group      125 181
Creation operators      147 206
Cycle notation      17
Cycle structure      17
Cyclic group      13
Degenerate representation      27
Dihedral group      14 213
Dimension of group representations      27
Dirac equation      203 210
Dirac spinor      230 326
Direct product of operators      49
Direct product of representations      49 117
Direct product of vector spaces      265 270 276
Direct sum      297
Discrete rotational symmetry      10
Distributive law      296
Dotted contravariant index      265 325
Dotted covariant index      265 324
Dual basis      301
Dual diagram      281
Dual vector space      264 301
Dummy index      292
Einstein convention      292
Electric multipole      242
Electromagnetic 4-potential      147 189
electromagnetic field      117 147 189 327
Energy band      8
Energy gap      8
Equivalence of group representations      32
Equivalence of tensor representations      274
Equivalence relation      19 296
Euclidean group      152
Euclidian group in three dimensions      166 223
Euclidian group in two dimensions      154 218
Euler angles      97
Event      174
Extended Euclidean group in two dimensions      218
Extended Euclidian group in three dimensions      223
Extended Poincar group      231
Fermi — Dirac system      134
Field operator, relativistic      203
Final state interaction      261
Four-group      13
Four-momentum operator      183
Four-vector      177
Four-vector, length of a four-vector      174
Four-vector, light-like      179
Four-vector, space-like      178
Four-vector, time-like      178
Fourier generalization of      134
Fourier series      8
Fourier theorem      8 91
Full Poincare group      246
Fundamental representations of the general linear group GL(m)      264
Fundamental representations of the Lorentz group SL(2,C)      189 320
Future cone      178
Gauge Coulomb      147
Gauge invariance      10
General linear group      15 70 263
General linear group, real      277
Generators      84
Generators of Euclidean groups      154 166
Generators of Lie groups      289
Generators of rotation groups      84 99
Generators of the Lorentz group      183
Generators of translations      90 154 182
Group      5 12
Group Abelian      13
Group algebra      45 307
Group continuous      15
Group contraction      166
Group cyclic      13
Group definition      12
Group dihedral      14
Group factor      22
Group general linear      15
Group multiplication      12
Group multiplication table      12
Group multiplication, table of      13

Group non-Abelian      14
Group of linear transformations      27
Group of motion      152
Group of translations discrete      5
Group of translations in one dimension      90
Group orthogonal      16 214 283
Group permutation      16 64
Group point      10
Group quotient      22
Group semi-simple      21 290
Group simple      21
Group space      10
Group special linear      180 280 320
Group special unitary      16 125 283
Group symmetric      16 64
Group unitary      16 277
Hamiltonian      2 122 149 183 246 259
Hamiltonian interacting      149 259
Helicity      136 168 199 226 257
Helicity states      139 194 199 234
Hermitian conjugate      305
Hermitian metric tensor      278
Hermitian operators      305
Homogeneity of space      9
Homogeneity of space-time      174
Homogeneity of time      9
Homogeneous Lorentz group      174
Homomorphism      23
Ideal left      309
Ideal two-sided      313
Idempotent      299 310
Idempotent condition for inequivalence      311
Idempotent condition to be primitive      310
Idempotent essentially      310
Identical particles      64
Identity element of a group      12
Identity representation      28
Identity transformation      15
Induced representation      160 166 196
Infinitesimal transformations      Generators 83 183
Inner product      302
Inner product space      302
Internal symmetry      11
Intrinsic parity      218 226 232
Intrinsic spin      136
Invariant group integration measure of SO(2)      87
Invariant group integration measure of SO(3) and SU(2)      129
Invariant subgroup      20
Invariant subgroup Abelian      21
Invariant subgroup of Euclidean groups      160 168
Invariant subgroup of the PoincarS      182
Invariant subspace      33
Invariant subspace irreducible      35 56
Invariant subspace minimal      33
Invariant subspace proper      33 35
Invariant tensors      95 175 262 267 270 278 280
Inverse      12
Irreducibility, necessary and sufficient condition of      45
Irreducible representations of Abelian groups      37
Irreducible representations of Euclidean groups      158 169 220 225
Irreducible representations of general linear groups      77 274 276
Irreducible representations of orthogonal groups      217 223 285
Irreducible representations of rotation groups      85 105
Irreducible representations of special linear groups      189 281
Irreducible representations of symmetric groups      70
Irreducible representations of the Lorentz group      187 191 230
Irreducible representations of the Poincare group      193 196 198 199 233 235
Irreducible representations of unitary groups      280
Irreducible set of basis vectors      54
Irreducible set of fields      114
Irreducible set of operators      60 115
Irreducible set of wave function      114
Irreducible tensors      60 115
Irreducible tensors of SO(3) and SU(2)      128
Isomorphism      17 296
Isotopic spin invariance      11
Isotropy of space      10
Isotropy of space-time      174
Kernel      24
Klein — Gordon equation      204
Lattice one-dimensional      2
Lattice rotational symmetry on      10
Lattice translational symmetry on      10
Left coset      21
Left ideal      309
Left ideal minimal      309
Length of four-vectors      174
Length of vectors      302
Lie algebra of Euclidean groups      155 167
Lie algebra of the PoincarS group      185
Lie algebra of the proper Lorentz group      186
Lie algebra of the rotation group      101—102
Lie group      80 290
Light-cone      178
linear combination      296
Linear dependence      296
Linear functional      265 301
Linear independence      296
Linear momentum basis      plane wave states
Linear momentum operator      93
Linear transformation      297
Linear transformation, symmetry-preserving      78 316
Linear vector space      295
Little group      160 168 180 193 196 199
Lorentz boost      176 184
Lorentz group, complete      227
Lorentz group, finite dimensional representations of      188
Lorentz group, inhomogeneous      181
Lorentz group, proper      177
Lorentz group, unitary representations of      189 328
Lorentz invariant      323
Lorentz scalar      323
Lorentz transformation 10      174
Lorentz transformation as “rotation” in x-t plane      177
Lorentz transformation special      176
Lorentz vector      177
Lowering operator      103 157
Magnetic multipole      242
Mass      192
Matrix group      15
Maxwell equations      202
Metric Minkowski      174
Metric tensor      174 278
Minkowski metric      174
Minkowski space      177
Mirror image      213
Mirror Symmetry      10
Momentum operator      155
Momentum operator linear      93
Momentum vector      168 193
Multiplication group      12
Multiplication of linear transformations by a number      298
Multiplication of vector by a number      295 298
Multipole electric      149
Multipole magnetic      149
Multipole moment operators      150 241
Multipole radiation      147 240
Multipole wave function      149
Negative energy solutions      205
Neutrino      199 237
Nilpotent      299
Non-Abelian group      14
Norm of vectors      302
One-cycle      17
Operator      297
Operator identity      298
Operator invertible      299
Operator null      298
Operator vector      115
Order of a group      13

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