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¬eld, 297 inverse, 66
¬‚uctuation“dissipation relation, 180 kinetic, 67, 72
¬‚uctuation“dissipation theorem, 70, 72, Lesser, 63
171, 450 matrix, 122
¬‚ux ¬‚ow regime, 462 one-particle, 22
¬‚ux quantum, 427 phonon, 66
Fock space, 15 quasi-classical, 199
free energy, 50, 290 retarded, 66, 513
free particle density of states, 522 single-particle, 62
free particle propagator, 515 symmetric matrix, 280
functional derivative, 272 time-ordered, 65, 81
functional determinant, 317 trajectory, 240
functional integral, 314 two-particle, 64
restricted, 330 Green™s function technique
functional integration, 313 standard diagrammatic impurity, 377
fundamental dynamic equation, 279 Green™s operator
advanced, 517
gauge invariance, 14 retarded, 517
gauge transformation, 231 Green™s operators, 515, 518
Gaussian integral, 315
Hamilton™s function, 61, 504
Gell-Mann“Low theorem, 83
generating functional, 69, 103, 270, 281, Hamiltonian, 3, 36
grand canonical, 72
317, 320
Hartree approximation, 470
generator of 1PI-vertices, 299
generator of connected amplitudes, 284, Hartree diagrams, 110
Heisenberg picture, 57
290
generator of connected Green™s functions, hermitian conjugation, 318
hermitian operator, 9
322
high-temperature superconductors, 476
generator of cumulants, 290
Ginzburg“Landau regime, 247
identical particles, 6
Gorkov equations, 224
imaginary-time, 140
gradient approximation, 184
imaginary-time formalism, 140
Grassmann ¬eld, 319
imaginary-time propagator, 506, 515
Grassmann algebra, 282
impurity correlator, 106
Grassmann variable, 282, 319
impurity scattering, 188
function of a, 319
inelastic di¬erential cross section, 175
Green™s function, 4, 62
inelastic scattering rate, 409
advanced, 67
in¬‚uence functional, 508
anomalous, 224, 357
interaction picture, 82
anti-time-ordered, 65
inverse propagator, 261
closed time path, 87
irreducible vertex functions
contour ordered, 87, 90
one-particle, 298
534 Index


Jacobian, 316, 459 mean free path, 193
jellium model, 45 Meissner e¬ect, 460
Johnson noise, 172 melting curve, 496
Joule heating, 169 mesoscopic ¬‚uctuations, 442
mesoscopic sample, 437
Kadano¬“Baym equations, 148 metal“insulator transition, 373, 376
kinematic momentum, 40 Migdal™s theorem, 200, 218
kinetic energy operator, 36 mixed coordinates, 68, 181
kinetic equation mixture, 48, 56
classical, 188 momentum operator, 35
kinetic propagator, 395 monomial, 282
Kramers“Kronig relations, 75, 158, 182, multi-particle space, 15
518 multiplication in parallel, 147
Kubo“Martin“Schwinger boundary con- multiplication in series, 146
ditions, 140 multiplication rule, 259
Lagrange density, 321 N -state amplitude, 258, 261
Lagrange™s function, 505 N -state diagram, 258
Landau criterion, 191, 209 Nambu ¬eld, 225
Landau gauge, 423 Nambu space, 225
Landau“Boltzmann equation, 209 Nernst“Ettingshausen e¬ect, 215
Langevin equation, 450 neutron scattering, 175
Legendre transform, 300 Noether™s theorem, 512
Legendre transformation, 505 normal state, 301
Lindemann criterion, 495 normal-ordered, 43
linear response, 151 normalization condition, 235, 242
local density of states, 520 number operator, 19, 24
localization, 388 total, 38
localization length, 375, 385 Nyquist noise, 173, 418, 437
London equations, 460
longitudinal phonons, 45, 71 occupation number representation, 29
loop expansion, 331 Ohm™s law, 172
Ohmic environment, 453, 510
magnetic impurities, 224, 233 one-body operator, 34
magnetic length, 402, 424 one-parameter scaling theory, 374
magnetic moments, 37 one-particle irreducible, 113, 114, 296
magneto-¬ngerprint, 446 vertices, 296
magneto-resistance, 424 operator
anomalous, 426 antisymmetrization, 7
Markov process, 192, 193 symmetrization, 7
master equation, 168 optical mass, 207
matrix element, 3 order parameter, 219, 223, 224, 235, 246
matrix Green™s function, 122
inverse free, 125 pair correlation function, 23
Matsubara frequency, 141 pair creation, 112
maximally crossed diagrams, 378 pair-breaking parameter, 251
mean ¬eld theories, 350 paramagnetic current, 40
Index 535


particle“hole space, 225 real rules, 134
particle“hole symmetry, 201 real-time contour, 93
partition function, 4, 49, 290 renormalization, 205, 207, 257, 306
path integral, 504 optical mass, 207
Pauli™s exclusion principle, 7, 22 resistance, 159, 169
Pauli™s master equation, 190 resistance tensor, 159
Peierls instability, 231 response function
phase coherence length, 410 current-current, 156
phase relaxation density-density, 153
rate, 437 road diagram, 286
time, 410
phase-breaking rate, 409, 410, 413, 415, s-wave scattering length, 358
scalar product, 2
421
scaling function, 375
phonon, 26, 28, 46
scaling theory of localization, 374, 445
phonon ¬eld, 66
scattering experiment, 174
phonon ¬eld operator, 46
Schr¨dinger picture, 56
o
phonon Hamiltonian, 26
Schr¨dinger equation, 3, 13, 54
o
photon, 47
screening, 383, 433
pinning, 462
second quantization, 27, 61
pinning force, 463, 469, 472, 475
self-averaging, 437, 445
pinning potential, 463
self-consistent approximations, 350
plane wave, 2
self-energy, 114, 117, 119, 302
Poisson bracket, 185, 213
impurity, 188
polarization, 433
matrix, 135
polarization vector, 47
skeleton diagrams, 118
Popov approximation, 362
skeleton diagrams
principle of least action, 505
two-particle irreducible, 118
probability amplitude, 258
Slater determinant, 10
propagator, 4
Sommerfeld model, 44
advanced, 514
sound velocity, 25
bare, 255
spectral function, 68, 515, 520
free, 255
spectral operator, 518
retarded, 513
spectral representation, 182, 518
quanta, 28 spectral weight function, 68, 75, 139, 180,
quantum electrodynamics, 28 185, 509
quantum ¬elds, 21 spin, 37
quantum kinetic equation, 179, 202, 233, spin-¬‚ip scattering, 233
236 spontaneously broken symmetry, 301
quantum of action, 3 state label, 255
quantum phase transition, 377 stationary state, 153
quantum statistics, 262 statistical operator, 48
quasi-particles, 46 thermal equilibrium, 49
quenched disorder, 93 strong localization, 375, 387
structure factor
radiation gauge, 29 dynamic, 177
ray, 2
536 Index


superconductivity, 217 von Neumann equation, 56
strong coupling, 224
Ward identity, 512
super¬‚uid velocity, 232
wave function, 2
superposition principle, 110, 259, 260, 322,
weak localization, 387
428, 505
weak-localization, 391
symmetric representation, 128
e¬ect, 378, 389, 445
symmetric subspace, 9
regime, 402
t-matrix, 359 Wick™s theorem, 95, 96, 324, 326, 328
tadpole diagram, 266 Wiener measure, 197
tadpole diagrams, 110, 460 Wigner coordinates, 68, 181
thermal equilibrium, 49, 165 Wigner function, 187
thermo-¬eld approach, 122
zero-bias anomaly, 430
thermodynamic potential, 51
thermodynamics, 4
third rank vertex, 126
three-line vertex, 113
time-dependent Ginzburg“Landau equa-
tion, 248
time-dependent Gross“Pitaevskii equation,
363
time-ordering, 55
trace, 49
transformation function, 503
transient phenomena, 92
transition force, 495
transition operator, 34
transport relaxation time, 164, 191
tree diagrams, 299, 331
triagonal representation, 128
triagonal representation, 129
two-body interaction, 42
two-body potential, 42
two-particle interaction, 13, 64, 130
two-particle irreducible vertices, 341
two-particle source, 339

unitary operator, 3
unlinked diagrams, 260
Usadel equation, 244

vacuum diagrams, 266, 270, 280, 293, 326
vacuum state, 15, 37, 38, 43, 55
vertex, 257
two-particle irreducible, 342
vertices
bare, 256

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