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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 |
 valued measure 163
 -meson 268
 Fourier transform 394
representation 81 384 385
Abelian extension 318
Absolute temperature 279 286
Adele 323 328
Adele group 40 338 347 388 393
Adele group of algebraic group 346
Adele group of semi-direct product 353
Adele group, Archimedean component 344
Adele group, non-Archimedean component 344
Adele, principal 388
Adiabatic curve 276
Adjoint representation 101
Algebraic group 323
Algebraic integer 314
Algebraic number field 313 314 317 346
Algebraic number field, additive group of 340
Algebraic number field, multiplicative group of 340
Almost periodic function 151 304 333 334
Alternating group 94
Amenability 157
Analytic Borel group 33
Analytic Borel space 32
Analytic function 306 307
Analyticity, causality and 248
Annihilator 41
Anti-commutation relations 257 258
Anti-particle 260
Anti-symmetric reduction 224 228
Artin L series 327
Asymptotic formula(s) 320 321 322 329
Asymptotic formula(s) for eigenvalues 296 297
atom 230 234
Atom in Boolean algebra of projections 55
Atomic spectra 234
Atomic weight 231
Autocorrelation coefficient 333
Autocorrelation function 150 152
Automorphic form 128 248 358 361 362 370 372 380 382 383 387
Automorphic forms of non-integral weight 379
Automorphic function 312 357 358
Automorphism of Hilbert bundle 64
B-N pair 129
Binary quadratic form 312 315 316
Binding energy 228
Black body radiation 293
Bochner — Herglotz theorem, generalized 148
Bohm — Aharonon effect 211
Bohr — Fourier series 304
Boltzmann's constant 286 295
Borel cocycle 140
Borel cross section of Hilbert bundle 50
Borel function 31
Borel G-space 33
Borel group 33
Borel Hilbert bundle 49
Borel set 30
Borel space 31
Borel structure 33 52
Borel subgroup 98 110
Bose — Einstein statistics 225
Boson 225 229 257
Boson field 299
Bound state 219 220 228 230 233 244
Bound states, interaction of 226 227
Boundary of homogeneous space 363
Branching law 103
Brownian motion 152
Brownian motion, flow of 138
C* algebra 302
Canonical quantization 211
Carnot cycle 278
Cartan subgroup 98 109 132
Cauchy integral formula 308
Causality and analyticity 248
Center of algebra 19
Central decomposition 57
Chance variable 143
Chaos 144 145 147 149
CHARACTER 5 10 20 25 36 38
Character group 38
Charge 214 250
Charge number of nucleus 229
Circle method 320
Class field theory 313 318 338
Class function 19
Class number 314 315 317
Classical Hamiltonian 206
Classical limit 204 206 207 265
Classical mechanics 160 163
Classical statistical mechanics 166 232
Clebsch — Gordon formula 103
Cohomology class 141
Commutative subgroup 98
Commutativity, local 266
Commuting algebra 11 238
Compactification of homogeneous space 364
Compactification of Riemann surface 358
Complementary series 372
Complementary subrepresentation 14
Complete Boolean algebra of projections 56
Complex simple Lie group 90
Complex vector bundle 118
Complexification of Lie algebra 89
Congruence 313
Congruence subgroup 356
Conjugate class 19
Connected Lie group 87
Conservation of energy, law of 170
Conservation of momentum, law of 172
Constant energy hypersurface 282
Constructive quantum field theory 269
Continuous center 55
Continuous direct sum 2
Continuous stationary stochastic process 152
Convolution 19
Correlation 147
Correlation coefficient 146
Coulumb forces 214
Covariance algebra 302
Cross section of Hilbert bundle 49
Crystal 231
Cusp 359 360 361 370 377
Cusp form 128 361 362 365 368 370
Cusp form as intertwining operator 371
Cyclic vector 147
Degenerate series 113
Differentiable chaos 144
Diophantine equation 313 328 353
Diophantine problems 317
Dirac field 260
Dirac quantization of electromagnetic field 254 256
Direct integral 2 49 51 72 135
Direct product of two groups 6
Direct sum of representations 8 10
Direct sum, infinite 35
Dirichlet series 300 303 315 316 321 323 324 328 329 330 331 372 376 381
Discrete series 120 123 127 370 372
Discriminant 314
Disjoint representations 12 35
Dispersion relations 242
Domain of positivity 310
Double coset intertwining operator 130 375 378
Dual group 38
Dynamical group 168 264
Dynamical group for one particle system 183
Dynamical variable 161
Eightfold way 104 268
| Einstein's formula for specific heat 294
Eisenstein integral 128
Eisenstein series 128 326 361 362 365 368 370 381 387 388
Eisenstein series for non-analytic automorphic forms 375
Eisenstein series, analytic continuation of 376 382
Eisenstein — Siegel series 389 390
Electric charge 214
electric field 250
Electrical forces 214
electromagnetic field 292
Electromagnetic waves 251
Electromagnetism 249
Electron 214 229 230 292
Electron mass 229
Electron positron field 260
Electron spin 229
Elementary particle 228
Elementary particles, symmetries of 267
Elliptic function 316 317
Energy Observable 169
Energy of formation of molecule 230
Energy operator 169
Energy, binding 228
Energy, free 280 290
Energy, internal 286
Energy, kinetic 208 209
Energy, potential 208 209
entropy 138 279 288 289
Equation of state 277
Equivalence of representations 10
Equivalence of unitary representations 34
Ergodic 66 133 136 137 263
Ergodic action 264 307
Ergodic invariant measure classes 134
Ergodic theorem(s) 134 151
Ergodic theorem(s), mean 135
Ergodic theory 269 302 303
Ergodicity, probabilistic significance of 148 149
Essentially transitive 134
Ether 251
Euclidean group 115 171 199 238 269
Euclidean invariance 175 180 182 204 238
Euler product 299 316 321 381
Exceptional complex Lie algebra 91
Exceptional Lie algebra 93
Exceptional Lie group 94
Exchange forces 228
Excited state 230
Expected value of observable 167
Factor 62
Factor representation 63
Fermi — Dirac statistics 225
Fermion 225 229
Field of force 249
Fields, interactions between 258
Finite simple group 93
First law of thermodynamics 275 276
force 209
Fourier transform in complex domain 309
Free energy 280 290
Frobenius reciprocity theorem 70 371
Functional equation 321
Functional equation for zeta function 316
Fundamental domain 358
Fundamental particle 228
G-bundle isomorphism 64
G-space 1
Galilean group 191 198 238 251 255
Galilean invariance 198 201 207 214 238 240
Galilean relativity 186 189 190 198 233
Gas 232
Gauge field 271
Gaussian integer 314 317
Gelfand — Harish Chandra principle 131 132
Generalized character 304
Generalized Fourier transform 43 44
Generalized harmonic analysis 152
Generalized harmonic analysis of Wiener 333
Generalized Poisson summation formula 325
Generating function 320 321 324 328 329
Genus of quadratic form 387
Gleason's theorem 166 194
Global class field theory 339
Grand partition function 332
Gravitational forces 214
Groessencharacter 323
Ground state 221 230
Group algebra 19
Group representation 3
Group velocity 188
Haar measure, left invariant 31
Hadron interactions 270
Hamiltonian form 206 208
Hamiltonian operator 169
Hardy — Littlewood results in Waring's problem 334 354 360 362
Harmonic analysis of sample functions 152
harmonic oscillator 291 292 294
Hasse principle 338
Heat 272
Heat, quantity of 274
Heat, specific 274
Hecke operator 371 372
Heisenberg commutation relations 180 181 182 260
High temperatures, agreement of classical and quantum statistical mechanics at 292
Higher reciprocity law 318
Highest weight of representation 99
Hilbert bundle 49
Hilbert G bundle 64 140
Hilbert space 34
Holomorphic cross sections 119
Homogeneous chaos 144 145 146 264
Homogeneous space, boundary of 363
Horosphere 377
Horospherical method 130 378
Horospherical subgroup 377
Hurwitz integral 83
Ideal 314 317
Ideal class 317
Ideal of Lie algebra 89
Idele group 322 323 339 346
Identity of particles, significance of 224 225
Imprimitivity theorem 72 175 181 200 201 248
Imprimitivity, system of 71 175 181 248 262
Imprimitivity, transitive system of 217
Independence of random variables 143
Index theorem 130
Indistinguishability of particles 257
Induced representation 179 385
Induced characters 353
Induced ergodic action 140
Induced representation 65 67 69 175 234 325 341 342 363 373 378
Induced representation, character of 348 349 374
Inducing in stages 71 368
information 284
Information theory 138 295
Inhomogeneous Lorentz group 252 259 265
Inner Kronecker product 27 28
Inner Kronecker product of induced representations 234
Integral of motion 170
Integrated periodogram 152
Interacting particles 281
Interaction between quantum mechanical particles 201
Interaction law 228
Interaction operator 216
Interactions between fields 258
Internal energy 286
Intertwining number 11
Intertwining operator 11 145 146 147 156 237 263 264 366 369 370 381
Intertwining operator for induced representations 365
Intertwining operator for unitary representations 34
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