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| Авторизация |
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| Mackey G. — Unitary Group Representations in Physics, Probability and Number Theory |
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| Предметный указатель |
Invariant measure in Borel G-space 33
Invariant probability measure 282
Invariant static quantization 264
Invariant subspace 10
Invariant subspace for unitary representations 34
Irreducible character 26
Irreducible representation 11
Isomorphism of Borel spaces 32
Isomorphism of Hilbert bundles 64
Isotope 231
Isotopic spin 268
Iwasawa's theorem 122
Joint probability distribution 143
kinetic energy 208 209
Koopman representation 135
Kronecker product of group representations 25 200
Kronecker product of group representations, inner 27 28
L function 319 320 321
Langlands' conjecture 130
Laplace transform 305 306 329
Large numbers, law of 150
Laurent series 306
Law of conservation of energy 170
Law of conservation of momentum 172
Law of Large Numbers 150
Lie algebra 87 88
Lie algebra, ideal of 89
Lie algebra, positive root of 101
Lie group 87
Lie group, connected 87
Lie group, real 109
Light, dual nature of 256
Light, velocity of 250
Linear momentum 171
Liouville measure 282
Liquid 232
Local class field theory 339
Local commutativity 266
Locally compact topological group 30
Locally isomorphic 88
Lorentz group 117 252
Lorentz group, inhomogeneous 252 259 265
Low temperatures, failure of classical statistical mechanics of 292
Magnetic field 249 250
Mandelstam theory 242
Mass number of nucleus 229
Maxwell's equations 250 251 253 255
Mean erogodic theorem 135
Mean value of sample function 149
Measure 31
Measure class 33
Mellin transform 330
Meromorphic function 358
Metiically standard Borel space 32
Metrically transitive 66
Michelson Morely experiment 251 253
Modular forms 320 321 322 328 329 331 354 359 360 372
Modular function 357
Molecule 230 234
Moller wave matrix 247
Momentum transfer 241
Multi-channel scattering 248
Multiplicity 13 341
Multiplicity free 243
Multiplicity free projection valued measure 46
Multiplier 80 200 380
Multiplier group 81
Multiplier system 380
Multipliers for semi-direct products 177
n-ary quadratic form 313 317 318
n-particle quantum system 199
Negative root of Lie algebra 101
Neutron 232 236 268
Nil radical 129
Non-abelian class field theory 381
Nonanalytic automorphic form 128 372 373
Noncommutative adele groups 131 381
Nuclear physics 232
Nuclear structure 234
Nucleon 236
Nucleus 229 230
Number theory, physical interpretation of results, in 298
Observable 160 161 163
Old quantum theory 160 232 292
One-dimensional character 26
One-parameter subgroup 87
One-parameter symmetry group 171
One-particle axiomatics 198
Operator valued distributions 266
Orbit 1
Orbital angular momentum 177
Ortho-complementation 161 162
Ortho-complemented partially ordered set 162
Orthogonal complement 14
Orthogonality relation 7
P wave scattering 244
p-adic analog of semi-simple Lie group 131
p-Adic integer 40 319 336
p-adic number 40 93 319 322 328 337 339 347
Parabolic subgroup 129
Partial wave amplitude 244
Partially ordered set 23 161 162
Particle multiple t 268
Particles, identity of 224 225
Particles, indistinguishability of 257
Particles, interacting 281
Partition 321
Partition function 289 290 291 297 299 301
Partitions of integer 320
Pauli exclusion principle 224 232
Perfect gas 291
Perfect predictability 151
Peter — Weyl theorem 36 83 151
Phase shift 244
Phase space 281 282
Phenomenological state 282
Philosophy of cusp forms 128
Photon 256 259
Plancherel formula 83 127 130
Plancherel measure 127 351
Plancherel measure class 110
Plancherel theorem 351
Planck's constant 170 210 294
Planck's discovery 294
Planetary motion 213
Poincare group 252 255
Poisson integral 364 365
Poisson integral as intertwining operator 368
Poisson summation formula 324 349 350 353 355 387 390
Pontryagin duality 38
Pontryagin — van Kampen duality 83
Position observables 202 203 210 225
Positive definite function 147
Positive definite quadratic form 324
Positive root of Lie algebra 101
Positron 259
potential energy 208 209
Prediction theory 150
Prediction, imperfect 150
Prediction, perfect 150
Pressure 277
Primary representation(s) 12 55 63
Prime 314 321
Prime ideal 317 322
Prime number theorem 300 318
Primes, distribution of 316
Principal adele 322 388
Principal ideal 317
Principal series 111 372 373
Probability amplitude 239 241
| Probability measure 282
Probability measure on ortho-complemented partially ordered set 162
Probability measure, invariant 282
Probability space 145
Process with independent increments 156
Products of ergodic actions 138
Projection valued measure 44 166 262
Projective multiplier 379 384
Projective representation 80 379 384
Properly ergodic 158
Proton 229 236 268
Proton mass 229
Proton spin 229
Pure point spectrum 135 151
Pure state 165
Quadratic form 346 383 393
Quadratic reciprocity law 313 315 391 392 393
Quanta of field 257 258
Quantization of fermion field 258
Quantization of interacting fields 260
Quantization, invariant static 264
Quantization, second 257
Quantization, static 262 263
Quantized electromagnetic field 259
Quantized electron field 259
Quantum chemistry 230 231
Quantum field theory 260 ff.
Quantum field theory, constructive 269
Quantum mechanical particles, interaction between 201
quantum mechanics 160 163 292
Quantum refinement of classical systems 208 209
Quantum statistical mechanics 166 232 332
Quantum theory, old 160 232 292
Quark 270
Quasi-discrete spectrum 157
Quasi-equivalence for primary representations 58
Quasi-invariant measure 34
Quaternionic Hilbert space 198
Quotient representation 11 35
Radiation, black body 293
Radon transform 378
Radon — Nikodym derivative 33
Random field 158
Random variable 143
Randomness 284 286 288 295
Rayleigh — Jeans law 232
Rayleigh's formula 293
Real form of complex Lie algebra 89 93
Real Hilbert space 194 198
Real Lie group 109
Reduction theory 314 317
Regge pole 242 245
Regge recurrence 245
Regge trajectory 245
Regular representation 368
Regularly related 125
Relativistically invariant quantum field 266
Relativity, Special Theory of 251
Representation of Lie algebra 97
Representation, highest weight of 99
Representation, induced 65 67 69 175
Representation, induced  (representation) 385
Resonance 245
Rest mass 186
Riemann surface 357 358
Riemann zeta function 299
Right invariant Haar measure 31
Right regular representation 14
Ring of operators 62
Root of Lie algebra 101
S operator 237
S operator, invariance properties of 237
S valued observable 175
S wave scattering 244
Sample function(s) 146 148 149 151
Sample function(s), harmonic analysis of 152
Scattering 235
Scattering experiments 236
Scattering operator 237 247 382
Scattering operator, analytic properties of 382
Scattering theory 236 247 381 382
Scattering theory of Lax and Phillips 382
Schroedinger equation 169 210 211
Schur's lemma 12 35
Second degree character 391 392 393
Second degree character as one-dimensional projective representation 394
Second law of thermodynamics 278 287
Second quantization 257
Selberg trace formula 129 324 349 372 374 382
Self-adjoint operator 166
Semi-direct product 74 340 342 343 347
Semi-simple Lie group 325 326
Semi-symmetric powers of representation 106
Semiconductor 232
Separable 30
Separable Hilbert space 34
Siegel formula 388
Siegel formula, (generalized) upper half plane 310 362 383
Siegel formula, upper half plane 310 362
Similarity of ergodic actions 141
Simple group 86
Simple Lie algebra 89
Singular series 335 336
Solid state theory 232 234
Solution number 341
Solvable group 98
Space-time 190
Special relativity 190 233
Specific heat 274
Specific heat of solid 291 292
Spectral multiplicity theory 84
Spectral theorem 84 166
Spectral theorem for representations of locally compact commutative groups 45
Spectral theorem for self adjoint operators 45
Spectrum of ergodic action 135
Spectrum of non-stationary stochastic process 156 157
Spin 177 182
Spin angular momentum 177
Spontaneous symmetry breakdown 271
Sporadic simple finite groups 95
Standard Borel G-space 145
Standard Borel space 32 143
Standard measure 53
State 160
State function 277
Static quantization, G-space invariant 262
Stationary stochastic process 143
Statistical ensemble 164
Statistical mechanics 231 281 292 300
Statistical mechanics, classical 232
Statistical mechanics, quantum 232
Statistical state 161 163
Stochastic process 143 156 157
Stochastic process with independent increments 156
Stochastic process, spectrum of non-stationary 156 157
Stone's theorem 170
Strange particle 268
Strictly ergodic 133 134 136 137
Strongly additive function 40
Sub-bundle 65 66
Subgroup theorem, for induced representation 124 126
Subrepresentation 11 35
Sum of observables 167
Supplementary degenerate series 113
Supplementary series 112 117
Surface harmonic 2
Surface harmonics 83
Symmetric group 94
Symmetric group, representation theory 105
Symmetric reduction 225 228
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