Absolute temperature 7—12 319
Analytic continuation 202
Anharmonic oscillator 311—313
Antisymmetry 278
Appel's comparison theorem 60 204
asymptotic freedom 174 197
Attraction basin 118 119
Auxiliary field 294
Backward velocity 336 n.
Baker — Hausdorf relation 262
Balance condition 342 350 n.
Bernoulli numbers 247
BHP theorem 155 165
Bohr — Sommerfeld equation 267
Boltzmann distribution 2 300
Bond moving 132—133
Borel sum 149 168 169
Bose statistic 275
Brillouin zone 34 200
Broken symmetry 13—17 114 183
Callan — Symanzik equation 152 168 172
Canonical transformation 248
Carlson theorem 179 n.
Casimir effect 253
Central limit theorem 113 323
Characteristic curves 152 172
Classical action 235 259
Classical equations of motion 258 260 310
Classical field 284 309
Classical Hamiltonian 1
Classical limit 235 257—282 300
Classical trajectories 265
Co-dimension 119
Computers 338
Confbrmal mapping 89
Connected correlations 53
Conservation laws 317 322
Conservation of energy 274
Continuity equation 329 336 n.
Convexity 131
Correlation functions 33—39 50 224 238—240
correlation length 36 121 225 286
Counterterms 73 167
Critical exponents 30 40 60 110 123 130 142 146—150 175—176 198
Critical exponents in four dimensions 173 174
Critical point 152 153 159
Critical surface 120
Cutoff 69 166 168 176—178
Decimation 132
Degeneration of the eigenvalues 223
Degree of divergence 84 165
Detailed balance condition 341
Determinant 246—248 249—253 260
Diagrams 52 58 61 77—80 107 109 212
Diagrams (two loops) 92—100 146
Diffraction 254 n.
Dimensional counting 74
Discrete spectrum of Hamiltonian 260
Disorder 320
dispersion relation 261
Dobrushin — Lanford — Ruelle equations 27
Droplet 203
Einstein relation 329
entropy 4 320
Equal-time commutation relations 241 284
Equal-time expectations 335
Equal-time Poisson brackets 284
Equations of motion 19 164 241—243
Equations of motion (classical) 1
Equilibrium probability 2
Ergodicity 317 341
Ergodicity threshold 322
Escape trajectories 121
Essential singularity 201
Eukr function 93—94
Euler — Maclaurin formula 247
Exponentially large time 273 324
Fermi energy 277
Fermi statistic 275
Fix point 118
Fix point stability 119 217
Fixed point 142 162 216
Fixed point hamiltonian 128 130 138 n.
Forward Langevin equation 327
Forward velocity 336 n.
Fotran program 342
Fourier transform 71
Free energy 3—4 121—123 185 222 244
Free energy, field dependent 186
Fugacity 214 2%
gap equation 212
Gas-liquid transition 215
Gaussian model 27 116 126 127 243
Goldstone boson 193
Goldstone — Salam — Weinberg theorem 192 206 n.
Grand partition function 214
Green functions 235 237 243 258
Ground state energy 244
Hamilton — Jacobi equation 235
Hamiltonian formalism 284
Hard spheres 316
harmonic oscillator 227—229 243—247
Hartree method 276
Heisenberg model 23
Heisenberg principle 249
Heisenberg representation 234
Helium 208 n.
high-temperature expansion 211
Hilbert — Schimdt operator 221 233 n.
Holder functions 254 n.
Imaginary time 240 249 275 301
Infinite dimensions 36 213 213—214
| Infinite volume limit 2 41—42 123 136 n.
information 6
Infrared divergences 105 169
Integral operator 221 230
intersection of two sets 138 n.
Intersections of random walks 297
Irreversibility 321
Ising model 23 46—48 59—64 130 207 n. 209 222 225 334
Ito differential calculus 336 n.
Jumping trajectory 272
Kubo — Martin — Schwinger condition 302 307 319
Large momentum region 150 154
Large-scale computations 338
Lattice spacing 70 229
Legendre transform 187
Lennard — Jones potential 339
Levinson theorem 270
Limiting cycle 137 n.
Linear response 12 33 303—307
Local operator 167
Long rang forces 205 nil
Longitudinal susceptibility 192 195
Lorentz group 283
low-temperature expansion 46—48 195—197
Markof chains 340
Mass 290
Mass gap 291 n.
Mass insertion 157
Massless theory 169
Maxwell relations 12
mean field 24—30 183 210 213
Mermin — Wagner theorem 188
Metric 283
Microcanonical distribution 3
Mixing 317
Momentum space 80
Monte Carlo renormalization group 138 n.
Non-Gaussian fixed point 135 136 140 146
Nonimeger dimensions 163
Noninteracting fermions 275
Nonrenormalizable theory 167
Normalization factor 230 233 n. 246
Number of bound states 264
O(N) invariant theory 108 146 147 161 n. 174 187—201 219
One line irreducible diagrams 187
Order 320
Oscillations in eigenvalue density 265—267
Periodic boundary conditions 222 301
Periodic trajectories 238
Perturbative expansion (asymptotic behavior) 149
Perturbative expansion, nonanalytic terms 160 162 n. 17
Phase shift 268
Planck formula 314
Poisson bracket 307
Poisson distribution 273
Poisson formula 101 313
Positivity condition 287
Power-law decay 201 205 n.
Proper time 298 n.
Pure states 17
Quantum Hamiltonian 234
Quantum probability distribution 300
Random force 326
Random numbers 342
Random potential 279
Random walk 54—58 293
Real gas 213—215
Recursion equation 113 134
Renormalizable 167
Renormalization conditions 141 170
Renormalization constants 141 142. 156 171
Renormalization group 144 171—173 181 n.
Renormalization group in momentum space 139 n.
Renormalized correlation functions 150 154 156
Renormalized coupling constant 141 159 198 216 226—227
Renormalized coupling constant, Monte Carlo determination of 161 n.
Renormalized field 141 170
Renormalized perturbative expansion 154—159
Resolvent of the Hamiltonian 261
Response function 303—304
Rigorous bounds 87
Running coupling constant 152 161 n. 173 177 200
Scaling corrections 144
Scaling laws 116 121—126 141 150—154 233 n.
Schrddinger equation 231 235 330
Self-energy 145 155 168
Self-repulsion of relativistic particles 296
square well potential 249
Stochastic differential equation 235
Subdiagrams 155 165
Superficial convergence 84
Superposition principle 236
Superrenormalizable theory 167
Surface tension 208 n.
Thomas — Fermi equations 277
Time dependent correlations 301
Time ordered product 239 242
Transfer matrix 221—232 288
Transfer matrix in many dimensions 232
Transition probability 340
Transversa] susceptibility 192
Truncation errors 350 n.
Tunneling probability 272
Two-body interaction 214 275
Typical trajectory 331
Ultraviolet divergences 72 83 144 165
Upper complex plane 306
Vacuum fluctuations 296
Variational Principle 6
viscosity 325
Watson theorem 87
Zero lattice spacing limit 73—75 178 198 229 298
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