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Fetter A.L., Walecka J.D. Quantum theory of many-particle systems
Fetter A.L., Walecka J.D.  Quantum theory of many-particle systems







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: Quantum theory of many-particle systems

: Fetter A.L., Walecka J.D.

:

"Singlemindedly devoted to its job of educating potential many-particle theorists ... deserves to become the standard text in the field." "Physics Today. "The most comprehensive textbook yet published in its field and every postgraduate student or teacher in this field should own or have access to a copy." "Endeavor. A self-contained treatment of nonrelativistic many-particle systems, this text discusses both formalism and applications. Chapters on second quantization and statistical mechanics introduce ground-state (zero-temperature) formalism, which is explored by way of Green's functions and field theory (fermions), Fermi systems, linear response and collective modes, and Bose systems. Finite-temperature formalism is examined through field theory at finite temperature, physical systems at finite temperature, and real-time Green's functions and linear response. Additional topics cover canonical transformations and applications to physical systems in terms of nuclear matter, phonons and electrons, superconductivity, and superfluid helium as well as applicati


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Fermi momentum      26
Fermi motion      193
Fermi sea      28 71
Fermi surface      179180 306 334
Fermi velocity      185
Fermi wavenumber      27 46
Fermi-gas model for nuclear matter      352357
fermions      1519
Fermis Golden Rule      189
ferromagnetism      32p
Feynman diagrams      96 378 399401 559562
Feynman diagrams, at finite temperature      241250
Feynman diagrams, in coordinate space      92100
Feynman diagrams, in momentum space      100105
Feynman rules, at finite temperature      242243 244248
Feynman rules, for bosons      208210 223p
Feynman rules, for electron-phonon system      399401
Feynman rules, for fermions      9799 102103
Feynman Dyson perturbation theory      112 113 115 399406
Field operators      19 65 71
Field operators, commutation relations of      19
Field operators, creation part      86
Field operators, destruction part      86
Field operators, equation of motion for      68 230
Field operators, for bosons      200
Finite-temperature formalism, $T      0
First quantization, relation to second quantization      15
First sound      184 481
Fission      351
Fluctuations      200 337p 527528
Flux quantization      415416 425 435436
Flux quantum      416 435
Fluxoid      423425 474p
Forward scattering      133
Free energy, Gibbs      34
Free energy, Gibbs, of magnetic systems      418
Free energy, Gibbs, of superconductor      432
Free energy, Helmholtz      34
Free energy, Helmholtz, of classical electron gas      280
Free energy, Helmholtz, of magnetic systems      418
Free energy, Helmholtz, of noninteracting phonons      393
Free energy, Helmholtz, of quasiparticles in He II      485
Free energy, Helmholtz, of superconductor      431 451 453 474p
Free surface in rotating He II      483
Frequency sums      248250 263 281
Friedel oscillations      179
Galitskiis equations      139146 358 370 373 376 567
Galitskiis equations, and Bethe Goldstone equations      377383
Gamma function      579580
gap equation      331 492
Gap equation, in nuclear matter      383385
Gap equation, infinite nuclei      531 535
Gap equation, normal solutions      332 531
Gap equation, superconducting solutions      333 446449 475p
Gap function      443 466474 489
Gapless superconductors      417n 46n0
Gauge invariance      444 454
Gell Mann and Low theorem      6164 113 208n
Giant dipole resonance      552
Ginzburg Landau parameter      435 472
Ginzburg Landau theory      430439 474
Ginzburg Landau theory, boundary conditions      432
Ginzburg Landau theory, coherence length      433 472
Ginzburg Landau theory, determination of parameters      471472
Ginzburg Landau theory, field equations      432 496n
Ginzburg Landau theory, flux quantization      435436
Ginzburg Landau theory, in one dimension      437
Ginzburg Landau theory, microscopic derivation of      466474
Ginzburg Landau theory, penetration length      434 472 475p
Ginzburg Landau theory, supercurrent      432
Ginzburg Landau theory, surface energy      436438
Ginzburg Landau theory, wave function      471
Goldstone diagrams      112 118p 354 376 381
Goldstones theorem      111116 387p
Gorkov equations      444 466
grand canonical ensemble      33 228
Grand canonical hamiltonian      228 256
Grand partition function      36 228 308p
Greens function      208
Greens function, heat capacity      42 43
Greens function, number density      39
Greens functions at zero temperature      6465 205 213 228 292 400
Greens functions at zero temperature, advanced      77
Greens functions at zero temperature, analytic properties      7679
Greens functions at zero temperature, as zero-temperature limit of real-time Greens function      293 296 308p
Greens functions at zero temperature, asymptotic behavior      79 297
Greens functions at zero temperature, at equal times      94
Greens functions at zero temperature, bosons      203 215
Greens functions at zero temperature, bosons, anomalous      213
Greens functions at zero temperature, bosons, hard-sphere Bose gas      220
Greens functions at zero temperature, bosons, ideal Bose gas      208
Greens functions at zero temperature, bosons, matrix Greens function      213214 501p
Greens functions at zero temperature, diagrammatic analysis in perturbation theory      92111
Greens functions at zero temperature, equation of motion      117p 411p
Greens functions at zero temperature, Feynman rules for, at finite temperature      see Temperature Greens functions)
Greens functions at zero temperature, Feynman rules for, in momentum space      102103
Greens functions at zero temperature, Feynman rules for, incoordinate space      9799
Greens functions at zero temperature, for electron-phonon system      399406
Greens functions at zero temperature, for ideal Fermi gas      7072
Greens functions at zero temperature, for interacting Fermi gas      145
Greens functions at zero temperature, for phonons      400 402404 410p 411p
Greens functions at zero temperature, frequency dependence of      75
Greens functions at zero temperature, Hartree Fock approximation      124
Greens functions at zero temperature, in interaction picture      85
Greens functions at zero temperature, matrix structure      7576
Greens functions at zero temperature, perturbation theory for      8385 96
Greens functions at zero temperature, physical interpretation      7982
Greens functions at zero temperature, real-time, at finite temperature      see Real-time Greens functions
Greens functions at zero temperature, relation to observables      6670
Greens functions at zero temperature, retarded      77
Gross Pitaevskii equation      496
Ground state in quantum-field theory      61
Ground-state energy, and Greens functions      68
Ground-state energy, and proper self-energy      109
Ground-state energy, and thermodynamic potential      289
Ground-state energy, electron-phonon system      399 411p
Ground-state energy, for bosons      31p 201 207 318
Ground-state energy, for bosons, hard-sphere bose gas      221222
Ground-state energy, Hartree Fock approximation      126
Ground-state energy, of electron gas      2526 32p 151154 281 289
Ground-state energy, of hard-sphere Fermi gas      132 135 148 374 387p
Ground-state energy, of ideal Fermi gas      27 46
Ground-state energy, of nuclear matter      353355 366377
Ground-state energy, shift of      70 109 111
Ground-state energy, superconducting and normal states      335
Ground-state energy, time-independent perturbation theory      31n 112 118p
Group velocity      183
Hamiltonian, first-quantized      4
Hamiltonian, models for physical systems, bosons      200 315
Hamiltonian, models for physical systems, electron gas      2125
Hamiltonian, models for physical systems, electron-phonon      333 391393 396398
Hamiltonian, models for physical systems, pairing force, in finite nuclei      523
Hamiltonian, models for physical systems, superconductors      439441
Hamiltonian, second-quantized      15 18
Hard-sphere Bose gas      218223 317319 480-481
Hard-sphere Bose gas, chemical potential      220 221222
Hard-sphere Bose gas, depletion      221 317
Hard-sphere Bose gas, Greens function      220
Hard-sphere Bose gas, ground-state energy      221222 318319
Hard-sphere Bose gas, other physical properties      222
Hard-sphere Bose gas, proper self-energies      219
Hard-sphere Fermi gas, chemical potential      147
Hard-sphere Fermi gas, effective mass      148 169p 370371
Hard-sphere Fermi gas, effective two-body interaction      136137
Hard-sphere Fermi gas, effective two-body wave function      137139
Hard-sphere Fermi gas, ground-state energy      135 148149 169p 374 387p 480
Hard-sphere Fermi gas, heat capacity      148
Hard-sphere Fermi gas, proper self-energy      136 142146 168p
Hard-sphere Fermi gas, single-particle excitations      146148
Hard-sphere Fermi gas, zero sound      195p 196p
harmonic oscillator      12 393 509511 569571
Hartree equations      127 490
Hartree Fock potential      355357 511 568
Hartree Fock theory      121127 167p 168p 399 475p 504508 575
Hartree Fock theory, at finite temperature      255259 262267 308p 415p
Hartree Fock theory, equations      126127 257258 507
Hartree Fock theory, equations, solution for uniform medium      127 258259
Hartree Fock theory, for bosons      259261
Hartree Fock theory, Greens functions      124 168p 257 308p 440441 475p
Hartree Fock theory, ground-state properties      126127 332
Hartree Fock theory, of finite nuclei      575
Hartree Fock theory, proper self-energy      121122 125 255258
Hartree Fock theory, relation to BCS theory      439441
Hartree Fock theory, self-consistency      121122 127 258259 265
Hartree Fock theory, single-particle energy      127 258 330 507 510 513 539 556
Hartree Fock wave functions      352353 503 508511 541 558559 567
Hartree Fock, and temperature Greens function      230 247 252
Hartree Fock, at finite temperature      258
Hartree Fock, of ideal quantum gas      39 46 49p
He II      44 481488
He II, critical velocity      482 488
He II, entropy      486
He II, heat capacity      44 484 486
He II, phase transition of      44 481
He II, quantized vortices      482484 488
He II, quasiparticle model      484488
He II, quasiparticle model, phonons      484488
He II, quasiparticle model, rotons      484488
He II, surface tension      498
He II, two-fluid model      481
Heat capacity, Debye theory of solids      393395
Heat capacity, of electron gas      269 289290p
Heat capacity, of hard-sphere Fermi gas      148
Heat capacity, of He II      44 484 486
Heat capacity, of ideal Bose gas      42 43
Heat capacity, of ideal Fermi gas      48
Heat capacity, of imperfect Fermi gas      261267
Heat capacity, of metals, Hartree Fock approximation      269 289p
Heat capacity, of metals, normal state      295n
Heat capacity, of metals, superconducting state      320 416 420 451454
Heisenberg picture      5859 73 173 189
Heisenberg picture, for bosons      204
Heisenberg picture, ground state      65 558
Heisenberg picture, modified, for finite temperatures      228 234
Heisenberg picture, operators      65 115 213 292
Heisenberg picture, relation to interaction picture      8385
High-energy nucleon-nucleus scattering      566
Hole-hole scattering      149150 381
Holes      7071 504508 514 520 524 538543 558-566
Homogeneous (uniform) system      69 190 214 292 321
Hugenholtz Pines relation      216 220 222 223p
Hydrostatic equilibrium      50p 111 195p 386p
Ideal Bose gas, chemical potential      3941 43
Ideal Bose gas, critical temperature      40
Ideal Bose gas, equation of state      39 42
Ideal Bose gas, occupation number      37
Ideal Bose gas, phase transition      44
Ideal Bose gas, statistical mechanics      3744
Ideal Bose gas, superfluidity      493
Ideal Bose gas, temperature Greens function      232234 245246 501p
Ideal Bose gas, thermodynamic potential      37 38
Ideal Bose gas, two-dimensional      49p
Ideal Fermi gas, chemical potential      45 48 75 284285
Ideal Fermi gas, density      2627 4547 352
Ideal Fermi gas, equation of state      45 46 4748
Ideal Fermi gas, Fermi energy      46
Ideal Fermi gas, ground-state energy      26 46
Ideal Fermi gas, heat capacity      48 266267
Ideal Fermi gas, occupation number      38
Ideal Fermi gas, paramagnetic susceptibility      49p 254p 309p
Ideal Fermi gas, statistical mechanics      4549
Ideal Fermi gas, temperature Greens function      232234 245246
Ideal Fermi gas, thermodynamic potential      38 278 285
Ideal Fermi gas, two-particle correlations      192
Imaginary-time operator      228
Imperfect Bose gas      see Hard-sphere Bose gas; Interacting Bose gas
Imperfect Fermi gas      see Hard-sphere Fermi gas; Interacting Fermi gas
Impulsive perturbation      180 184 307
Independent-pair approximation      357377 480
Independent-pair approximation, ground-state energy      368
Independent-pair approximation, justification      376
Independent-pair approximation, self-consistency      368
Independent-pair approximation, single-particle potential      368
Independent-particle model of the nucleus      352357 366
Independent-particle model of the nucleus, justification      376
Integral kernel for superconductor      456 458
Integral kernel for superconductor, in Pippard limit      463
Integrals, definite      579581
Intensive variables      35
Interacting Bose gas      215218 219 314319
Interacting Bose gas, chemical potential      216 336p
Interacting Bose gas, depletion      218 317
Interacting Bose gas, excitation spectrum      217 218 317
Interacting Bose gas, ground-state energy      318 336p
Interacting Bose gas, moving condensate      223p 336p 501p
Interacting Bose gas, near $T_{c}$      259261 493
Interacting Bose gas, proper self-energies      215
Interacting Bose gas, sound velocity      217 317
Interacting Bose gas, superfluidity      493
Interacting Fermi gas      128150 261267 326-336
Interacting Fermi gas, distribution function      333334
Interacting Fermi gas, effective mass      167p 266
Interacting Fermi gas, entropy      265266
Interacting Fermi gas, ground-state energy      27 118p 168p 319
Interacting Fermi gas, heat capacity      261267
Interacting Fermi gas, magnetization      32p 169p 310p
Interacting Fermi gas, proper polarization      169p 196p
Interacting Fermi gas, zero sound      183187 196p
Interaction picture      5458
Interaction picture, for bosons      207208
Interaction picture, for finite temperature      234236
Internal energy      34 247 251
Interparticle spacing      25 27 349 366 389 394 397
Irreducible diagram      403405
Irreducible tensor operator      505 508 543 586
Irrotational flow      425 481
Isotope effect      320 417 448 476p
Isotopic spin      353 508 546
Josephson effect      435n
kinetic energy      4 23 67 205 229
Kohn effect      411p
Kronecker delta      23
Ladder diagrams      131139 358 378379 567
Lagrange multiplier      203 486n 500p
Laguerre polynomials      509
Lambda point      481
Landau critical velocity      488 493
Landau damping      308
Landau diamagnetism      462 477p
Landaus Fermi liquid theory      187
Landaus quasiparticle model      484488
Legendre polynomials      516
Legendre transformation      34 336p
Lehmann representation, for bosons      214215
Lehmann representation, for correlation functions      299 300301 456
Lehmann representation, for Greens functions at zero temperature      66 7279 107
Lehmann representation, for polarization propagator      117p 174 300301 559
Lehmann representation, for real-time Greens function      293294
Lehmann representation, for temperature Greens function      297
Lifetime of excitations      8182 119p 146147 291 308 309p 310p
LIMIT      288289 293 296 308p
Linear response      172175
Linear response, at finite temperature      298303
Linear response, electron scattering      188194
Linear response, in finite nuclei      566 577p
Linear response, neutron scattering      196197p
Linear response, of charged Bose gas      501p
Linear response, of electron gas      175183 303308
Linear response, of superconductor      454466
Linear response, to weak magnetic field      309p 454466 477p
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