Amit D.J. — Field theory, the renormalization group, and critical phenomena :: Электронная библиотека попечительского совета мехмата МГУ

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Amit D.J. — Field theory, the renormalization group, and critical phenomena

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Название: Field theory, the renormalization group, and critical phenomena

Автор: Amit D.J.

Аннотация:

There are only very few textzbooks on the intermediate level, and the first edition of Amit's work has been a very useful one. The second edition with a detailed exposition on finite size scaling, universality and the critical behavior with several coupling constants promises to be a valuable tool in the library of many physicists.

Язык:

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: revised second edition

Год издания: 1984

Количество страниц: 394

Добавлена в каталог: 23.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\epsilon$ -emergence of      196—197
$\epsilon$ -expansion      197 208 214 219 220 228—266 274 277 280 312 320 333 335 342 364—365 373
$\hslash$       103 105
$\pi$ -subspace      367
$\sigma$ -model      107—108 174—196
$\sigma$ -model, interactions      370
$\sigma$ -model, linear      366
$\sigma$ -model, non-linear      366—381
$\sigma$ -model, partition function of      366
$\sigma$ -model, renormalization of      378—380
't Hooft, G.      xv 42 79 148 155 161 188 227 246 250—251 269
Abe, R.      146
Abers, E.S.      xv 34 52 102
Achiam, Y.      309
action      106 142 145 366 368 379
Aharony, A.      269 309 341
Ahlers, G.      269
Albeverio, S.      32
Amit, D.J.      102 146 188 269 341 363 381
Analytic continuation: in number of components      343
Analytic continuation: in number of dimensions      148 248 257
Analytic continuation: in time      34 40 41
Anisotropy      9 184 346 361
Anisotropy mass      182 183 346 361
Anisotropy-cubic      66 324—328 330 343
Antiferromagnetism      4 6 14 19 24 94
Aref'eva, I.Ya.      375 381
Ashkin, J.      32
Asymptotic: behavior      243 278—279 311 342 343 374 376—377
Asymptotic: behavior infrared      203 327
Asymptotic: behavior ultra violet      203
Asymptotic: freedom      201—205 219 229 240—243 374
Asymptotic: region      214 241 313 349 354
Azakov, S.I.      381
Baker, G.A.      32
Balian, R.      79 322
Barber, M.N.      308
Bardeen, W.A.      381
Bare parameters      14—15 164 321 352
Bare theory      162 190—192 212 214—217 220 227
Bare theory renormalization group equation for      214—217 227
Berezinskii, V.L.      381
Berlin, T.H.      32 104 146
Bervillier, C.      227 269 320 322
Bi-critical point      179 346—361
Bjorken scaling      204
Bjorken, J.D.      46 52 204
Bogoliubov, N.N.      xv 53 179 188
Born term      285 287
Bosons      67 94 185
boundary conditions      278
BPHZ procedure      179—184 188
Brezin, E.      xv 54 79 146 188 227 267 269 277 278 308 309 322 341 365 381
Brillouin zone      22 24
Broken symmetry      see “symmetry”
Bruce, A.D.      341
Burfod, R.J.      309
Callan — Symanzik equation      189 190 212 214 243—246
Callan — Symanzik equation homogeneous      214 226
Callan, C.G.Jr.      53 227
Callen, H.B.      102
Carneiro, C.E.I.      343 363
Characteristic equations      198 242 335 355
Characteristics, solution by      197—198 225 242 355 356
Charge      324
Chen, J.-H.      341
Coexistence: curve      5 314 318 364—365
Coexistence: region (two phase)      112
Coleman — Weinberg mechanism      274 324 330—339
Coleman, S.      10 32 102 145 188 199 227 229 269 341 365
Commutator, equal time      45
Compressibility      4
Confinements      204
Constraint on field magnitude      365—366
continuum limit      375
Contraction: in graphs      64 71 82 83
Contraction: tensorial      174 187 231 252
Coordinate space      54—66 72—74 106
Corrections, logarithmic      204—205 243
Correlation function, energy      21 199 210—212
correlation length      4 20 27 160 178 186 190 206—208 214 278 319 321 335
Correlation length of non-linear $\sigma$ -model      375
Correlation length, infinite      96 324 330—332
Correlation length, longitudinal      174
Correlation length, transverse      96 174 354 376
Correlations      3 11 96
Counterterms      167—169 174 179—185 186 348
Coupling constant: dimension of      149 171
Coupling constant: flow of      198 201—205 209 216—217 237—238 242 327—328 330—331 336 338 343 356
Coupling constant: negative      329—339
Coupling constant: several      274 328
Coupling constant: space      324
Coupling constant: temperature as      373—374
Critical: dimension, lower      274
Critical: exponents      4—9 14—15 27—28 108—109 132 200—201 205—212 217—218 228—266 278 310—311 316—318 347 349—350 376—377
Critical: exponents, exponents, effective      357—361
Critical: isochore      318
Critical: isotherm      318
Critical: line      170
Critical: mode      365
Critical: number of dimensions      148 154—157 169 171 229 240—243 248 281 329 373
Critical: phenomena      27 3
Critical: point      5 15 110 115 132 135 159—160 208 267 300 318 341 364 375
Critical: region      7 160 164—166 189—227 249 318 342 364
Critical: temperature      110 132 162 347
Critical: temperature, above      164—166 205—208 225 321 324
Critical: temperature, below      164 208—210 225 321 364
Critical: temperature, shift in      351
Critical: theory (massless)      162 190—199 200 211 215 229 250 303 324—337
Crossover      127 274 342—362
Crossover, exponent of      343 344 346—350
Crossover, function      343 350—361
Crossover, Gaussian to critical      343
Crossover, high to low symmetry      343
Crossover, high to low temperature      365 375
Crystaline order      339
Cutoff: dependence      114 117 119 123 147 189
Cutoff: dilation of      216
Cutoff: finite      115 117 119 122 186 238—240
Cutoff: intrinsic (microscopic)      15 24 113 117 147—148
Cutoff: scale of      216 227
David, F.      381
De Dominicis C.      87 102 146 309
DeGennes, P.G.      32
Density of bacteria      199
Derrida, B.      308
Des Cloizeaux, J.      32
Di Castro, C.      54 79
Diagramatic rules      60—61 66 71—72
Dilution, Lagrangian for      396
Dilution, probability      346
Dilution, quenched      346
Dilution, random      343
Dimension of space: above four      111 155 196 224
Dimension of space: below four      26—28 114—115 119—121 143 157 161 186 193 196—197 214 251 286
Dimension of space: continuation in      195—196 222 248
Dimension of space: critical      see “Critical number of dimensions”
Dimension of space: four      196 219 243 280 324
Dimension of space: lower critical      365
Dimension of space: one      365
Dimension of space: six      196
Dimension of space: three      242
Dimension of space: two      365 368—369 372—375 377 378
Dimension of space: upper critical      365
Dimension of x      241
Dimension of x, temperature      367
Dimensional analysis      148—150 152 153 158 180 185 193 196 198 201 206 211 212 238 282 287 313 318 379
Dimensional regularization      see “Regularization”
Dimensional transmutation      324
Dimensionful parameter      241 324 337 374

Dimensionless coupling      324 329—330 373
Dimensions of operators: anomalous      199—201 204 228 229 280—282 287 292 293 297 302 305 311 345 375
Dimensions of operators: canonical (engineering)      148—150 153 169 180 185 198 200 224 282—288 296 307 345 373
Dimensions of operators: composite      280—288 297 302
Dimensions of operators: matrix of      305
Dirac operator      43
Disordered state      see “Symmetric state”
Divergence: degree of      152—154 156
Divergence: infrared      372
Divergence: internal      120 125 152 179
Divergence: logarithmic      119—121 124—125 144 156 190 197
Divergence: primitive      151—157 169 179—180 185 231 248 279 306 372 380
Divergence: quadratic      118—119 125 162—163 169 283
Divergence: ultra-violet      119—123 143 152—158 162 185 279 372
Divergence: ultra-violet logarithmic      114 249 372
Dolan, L.      145
Domany, E.      188
Domb, C.      xv 8
Drell, S.D.      46 52
Droplet model      6
Dyson equation      86
Dyson, F.J.      33 53
Eigenvalue      302 304—306
Eigenvector, left      304 306
Einhorn, M.B.      341
Electrodynamics, scalar      14 181 324 329
Electromagnetic potential      329
Elitzur, S.      381
Emery, V.      341 363
Energy density      28 344
Energy, mean      20 21
Energy-energy interaction      343 344
entropy      3
Equation of state      5 93 208—210 243 267 311—315 321 364—365
Equation of state, renormalized      166 311—313
Equations of motion of Bose field      44
Equations of motion, renormalized      292 300—308
expectation value      324 368—369
Exponent: $\alpha$       5—9 28 109 212 236 298 318 320 343 344 346
Exponent: $\beta$       5—9 108 210 236 312—315 318—320 377
Exponent: $\delta$       5—9 31 209 312—315 318—320
Exponent: $\eta$       5—9 27 108 146 200—201 208—210 217 230—237 256 266 317—320 337
Exponent: $\gamma$       4—9 27 108 132 143 208 210 236—237 312 318—320 347
Exponent: $\nu$       4—9 27 108 201 206—208 218 233—236 255 266 317—320 377
Exponent: $\omega$       239 277 311
Exponent: $\phi$       301—305
Exponent: effective      357—361
Exponents      see “Critical exponents”
Extremum properties      92
fermions      43 67
Ferrer, M.      322
Ferro-electric      14
Ferro-magnetic coupling      18
Ferromagnet: dipolar      243
Ferromagnet: uniaxial      12
ferromagnetism      4 6 24
Feynman integral: analytic continuation of      195—196 223
Feynman integral: with cutoff      247—248 257—259
Feynman parameters      222 264
Feynman, R.P.      50 52
Field: boson quantum      41—52
Field: complex      12—14 182 329
Field: continuous      14 31 169
Field: dimensionless      368 376
Field: direction      331 333 337 340 367
Field: electromagnetic      14
Field: equation, classical      106
Field: equations, operator      42 44 48
Field: external      50 68 87 92—94 110 134 136 164 182 365 369 373
Field: external, magnetic      5 6 12 16—22 31 93—94 110 171
Field: external, staggered      4
Field: incoming      43 48
Field: massive vector      67
Field: multi-component boson      13 63—66 87 91—94 107—108 126 171—174 183 233—236 302 303 324—328 331 343 346 364—367
Field: non-abelian gauge      204—205
Field: order-parameter      11
Field: outgoing      48
Field: scale of      116 316 337 373
Field: space, internal      367
Field: theoretic methods      273 274
Field: theory: Euclidean      25—28 40 47 54
Field: theory: free      26—28
Field: theory: quantum      15 25 33—52 103 105 111—114 117 229
Field: vector      67
Field: with high spin      67
Fields, classical      87—96 106—108 134 139—142
Finite size      see “Scaling finite 274
Finite system      278 279
Fisher, M.E.      6 8 10 79 269 308 309 341
Fixed point: approach to      201—205 217
Fixed point: at $T_{C}$       278 377
Fixed point: cubic      327—328 344
Fixed point: domain of attraction      203 217 323 324
Fixed point: Gaussian      218—219 236 240 326
Fixed point: infrared stable      202—205 217 236 239—241 269—270 323 374—375
Fixed point: Ising      294 343 344 345
Fixed point: non-trivial      218 237—240 246 280 365 375
Fixed point: O(M)-symmetric (Heisenberg)      325—328 330 335 342 344
Fixed point: spherical      218
Fixed point: stability to high operators      282 291
Fixed point: stable      328 343
Fixed point: ultraviolet stable      202—203 237 240 374
Fixed point: zero-temperature      365 374—375 377
Flow diagram      328—331 342
Flow diagram equation      329 339
Flow diagram function $\beta$       311 330 337 339 374
Flow diagram, of bacteria      199
Flow diagram, on logarithmic scale      336
Flow diagram, topography      328 343
Flow diagram, trajectory      329 335
Fluctuations      7 8 11 14—15 29 82 103 109 113 332 365
Fluctuations, amplitude      365—367
Fluctuations, of $\pi$ -fields      367
Fluctuations, phase      365—366
Fock, space      48
Free energy      5—9 15 31 83 92—93 108 110 134 136 139—143 329 332—335 337
Free energy, bare      333
Free energy, divergences      333
Free energy, extremum      324 335
Free energy, one loop      333 340
Free energy, renormalized      333
Fresnel integral      36
Fried, H.M.      42 46 52
Functional: derivative      50
Functional: equation      303—304
Functional: integrals      16 18—27 33—41 367
Gas liquid system      94
Gauge invariance      67
Gauge theory, non-abelian      374 378
Gelfand, I.M.      32
Gell–Man, M.      33 53
Generating functional      26—27 68 303 373 378
Generating functional, divergent part of      379—380
Geometric description      337—339
Ginzburg criterion      109—111 143 277
Ginzburg, V.L.      145
Goldschmidt, Y.Y.      363 381
Goldstein, H.      102
Goldstone bosons      96 103 108 136 178 364—365 368 375
Goldstone bosons, theorem      87 94—96
Goldstone, J.      94 102
Golner, G.R.      269
Graph: faithful representation of      128—135
Graph: one particle irreducible      86—90 101 141 225 370
Graph: symmetry factor of (combinatorial)      61 65 73—74 77 99 109 143 174 231
Graph: tadpole      see “Tadpole”
Graph: vacuum      56—60 74 77 83 141 145
Graphs, Taylor expansion of      121 179
Green function: causal      41 46 52
Green function: connected      82—85 123 168 304 378

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