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Fetter A.L., Walecka J.D. — Quantum theory of many-particle systems
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Íàçâàíèå: Quantum theory of many-particle systemsÀâòîðû: Fetter A.L., Walecka J.D. Àííîòàöèÿ: "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
ßçûê: Ðóáðèêà: Ôèçèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2003Êîëè÷åñòâî ñòðàíèö: 601Äîáàâëåíà â êàòàëîã: 14.09.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Fermi momentum 26 Fermi motion 193 Fermi sea 28 71 Fermi surface 179—180 306 334 Fermi velocity 185 Fermi wavenumber 27 46 Fermi-gas model for nuclear matter 352—357 fermions 15—19 Fermi’s “Golden Rule” 189 ferromagnetism 32p Feynman diagrams 96 378 399—401 559—562 Feynman diagrams, at finite temperature 241—250 Feynman diagrams, in coordinate space 92—100 Feynman diagrams, in momentum space 100—105 Feynman rules, at finite temperature 242—243 244—248 Feynman rules, for bosons 208—210 223p Feynman rules, for electron-phonon system 399—401 Feynman rules, for fermions 97—99 102—103 Feynman — Dyson perturbation theory 112 113 115 399—406 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 527—528 Flux quantization 415—416 425 435—436 Flux quantum 416 435 Fluxoid 423—425 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 248—250 263 281 Friedel oscillations 179 Galitskii’s equations 139—146 358 370 373 376 567 Galitskii’s equations, and Bethe — Goldstone equations 377—383 Gamma function 579—580 gap equation 331 492 Gap equation, in nuclear matter 383—385 Gap equation, infinite nuclei 531 535 Gap equation, normal solutions 332 531 Gap equation, superconducting solutions 333 446—449 475p Gap function 443 466—474 489 Gapless superconductors 417n 46n0 Gauge invariance 444 454 Gell — Mann and Low theorem 61—64 113 208n Giant dipole resonance 552 Ginzburg — Landau parameter 435 472 Ginzburg — Landau theory 430—439 474 Ginzburg — Landau theory, boundary conditions 432 Ginzburg — Landau theory, coherence length 433 472 Ginzburg — Landau theory, determination of parameters 471—472 Ginzburg — Landau theory, field equations 432 496n Ginzburg — Landau theory, flux quantization 435—436 Ginzburg — Landau theory, in one dimension 437 Ginzburg — Landau theory, microscopic derivation of 466—474 Ginzburg — Landau theory, penetration length 434 472 475p Ginzburg — Landau theory, supercurrent 432 Ginzburg — Landau theory, surface energy 436—438 Ginzburg — Landau theory, wave function 471 Goldstone diagrams 112 118p 354 376 381 Goldstone’s theorem 111—116 387p Gorkov equations 444 466 grand canonical ensemble 33 228 Grand canonical hamiltonian 228 256 Grand partition function 36 228 308p Green’s function 208 Green’s function, heat capacity 42 43 Green’s function, number density 39 Green’s functions at zero temperature 64—65 205 213 228 292 400 Green’s functions at zero temperature, advanced 77 Green’s functions at zero temperature, analytic properties 76—79 Green’s functions at zero temperature, as zero-temperature limit of real-time Green’s function 293 296 308p Green’s functions at zero temperature, asymptotic behavior 79 297 Green’s functions at zero temperature, at equal times 94 Green’s functions at zero temperature, bosons 203 215 Green’s functions at zero temperature, bosons, anomalous 213 Green’s functions at zero temperature, bosons, hard-sphere Bose gas 220 Green’s functions at zero temperature, bosons, ideal Bose gas 208 Green’s functions at zero temperature, bosons, matrix Green’s function 213—214 501p Green’s functions at zero temperature, diagrammatic analysis in perturbation theory 92—111 Green’s functions at zero temperature, equation of motion 117p 411p Green’s functions at zero temperature, Feynman rules for, at finite temperature see Temperature Green’s functions) Green’s functions at zero temperature, Feynman rules for, in momentum space 102—103 Green’s functions at zero temperature, Feynman rules for, incoordinate space 97—99 Green’s functions at zero temperature, for electron-phonon system 399—406 Green’s functions at zero temperature, for ideal Fermi gas 70—72 Green’s functions at zero temperature, for interacting Fermi gas 145 Green’s functions at zero temperature, for phonons 400 402—404 410p 411p Green’s functions at zero temperature, frequency dependence of 75 Green’s functions at zero temperature, Hartree — Fock approximation 124 Green’s functions at zero temperature, in interaction picture 85 Green’s functions at zero temperature, matrix structure 75—76 Green’s functions at zero temperature, perturbation theory for 83—85 96 Green’s functions at zero temperature, physical interpretation 79—82 Green’s functions at zero temperature, real-time, at finite temperature see Real-time Green’s functions Green’s functions at zero temperature, relation to observables 66—70 Green’s functions at zero temperature, retarded 77 Gross — Pitaevskii equation 496 Ground state in quantum-field theory 61 Ground-state energy, and Green’s 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 221—222 Ground-state energy, Hartree — Fock approximation 126 Ground-state energy, of electron gas 25—26 32p 151—154 281 289 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 353—355 366—377 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 21—25 Hamiltonian, models for physical systems, electron-phonon 333 391—393 396—398 Hamiltonian, models for physical systems, pairing force, in finite nuclei 523 Hamiltonian, models for physical systems, superconductors 439—441 Hamiltonian, second-quantized 15 18 Hard-sphere Bose gas 218—223 317—319 480-481 Hard-sphere Bose gas, chemical potential 220 221—222 Hard-sphere Bose gas, depletion 221 317 Hard-sphere Bose gas, Green’s function 220 Hard-sphere Bose gas, ground-state energy 221—222 318—319 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 370—371 Hard-sphere Fermi gas, effective two-body interaction 136—137 Hard-sphere Fermi gas, effective two-body wave function 137—139 Hard-sphere Fermi gas, ground-state energy 135 148—149 169p 374 387p 480 Hard-sphere Fermi gas, heat capacity 148 Hard-sphere Fermi gas, proper self-energy 136 142—146 168p Hard-sphere Fermi gas, single-particle excitations 146—148 Hard-sphere Fermi gas, zero sound 195p 196p harmonic oscillator 12 393 509—511 569—571 Hartree equations 127 490 Hartree — Fock potential 355—357 511 568 Hartree — Fock theory 121—127 167p 168p 399 475p 504—508 575 Hartree — Fock theory, at finite temperature 255—259 262—267 308p 415p Hartree — Fock theory, equations 126—127 257—258 507 Hartree — Fock theory, equations, solution for uniform medium 127 258—259 Hartree — Fock theory, for bosons 259—261 Hartree — Fock theory, Green’s functions 124 168p 257 308p 440—441 475p Hartree — Fock theory, ground-state properties 126—127 332 Hartree — Fock theory, of finite nuclei 575 Hartree — Fock theory, proper self-energy 121—122 125 255—258 Hartree — Fock theory, relation to BCS theory 439—441 Hartree — Fock theory, self-consistency 121—122 127 258—259 265 Hartree — Fock theory, single-particle energy 127 258 330 507 510 513 539 556 Hartree — Fock wave functions 352—353 503 508—511 541 558—559 567 Hartree — Fock, and temperature Green’s function 230 247 252 Hartree — Fock, at finite temperature 258 Hartree — Fock, of ideal quantum gas 39 46 49p He II 44 481—488 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 482—484 488 He II, quasiparticle model 484—488 He II, quasiparticle model, phonons 484—488 He II, quasiparticle model, rotons 484—488 He II, surface tension 498 He II, two-fluid model 481 Heat capacity, Debye theory of solids 393—395 Heat capacity, of electron gas 269 289—290p 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 261—267 Heat capacity, of metals, Hartree — Fock approximation 269 289p Heat capacity, of metals, normal state 295n Heat capacity, of metals, superconducting state 320 416 420 451—454 Heisenberg picture 58—59 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 83—85 High-energy nucleon-nucleus scattering 566 Hole-hole scattering 149—150 381 Holes 70—71 504—508 514 520 524 538—543 558-566 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 39—41 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 37—44 Ideal Bose gas, superfluidity 493 Ideal Bose gas, temperature Green’s function 232—234 245—246 501p Ideal Bose gas, thermodynamic potential 37 38 Ideal Bose gas, two-dimensional 49p Ideal Fermi gas, chemical potential 45 48 75 284—285 Ideal Fermi gas, density 26—27 45—47 352 Ideal Fermi gas, equation of state 45 46 47—48 Ideal Fermi gas, Fermi energy 46 Ideal Fermi gas, ground-state energy 26 46 Ideal Fermi gas, heat capacity 48 266—267 Ideal Fermi gas, occupation number 38 Ideal Fermi gas, paramagnetic susceptibility 49p 254p 309p Ideal Fermi gas, statistical mechanics 45—49 Ideal Fermi gas, temperature Green’s function 232—234 245—246 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 357—377 480 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 352—357 366 Independent-particle model of the nucleus, justification 376 Integral kernel for superconductor 456 458 Integral kernel for superconductor, in Pippard limit 463 Integrals, definite 579—581 Intensive variables 35 Interacting Bose gas 215—218 219 314—319 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 259—261 493 Interacting Bose gas, proper self-energies 215 Interacting Bose gas, sound velocity 217 317 Interacting Bose gas, superfluidity 493 Interacting Fermi gas 128—150 261—267 326-336 Interacting Fermi gas, distribution function 333—334 Interacting Fermi gas, effective mass 167p 266 Interacting Fermi gas, entropy 265—266 Interacting Fermi gas, ground-state energy 27 118p 168p 319 Interacting Fermi gas, heat capacity 261—267 Interacting Fermi gas, magnetization 32p 169p 310p Interacting Fermi gas, proper polarization 169p 196p Interacting Fermi gas, zero sound 183—187 196p Interaction picture 54—58 Interaction picture, for bosons 207—208 Interaction picture, for finite temperature 234—236 Internal energy 34 247 251 Interparticle spacing 25 27 349 366 389 394 397 Irreducible diagram 403—405 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 131—139 358 378—379 567 Lagrange multiplier 203 486n 500p Laguerre polynomials 509 Lambda point 481 Landau critical velocity 488 493 Landau damping 308 Landau diamagnetism 462 477p Landau’s Fermi liquid theory 187 Landau’s quasiparticle model 484—488 Legendre polynomials 516 Legendre transformation 34 336p Lehmann representation, for bosons 214—215 Lehmann representation, for correlation functions 299 300—301 456 Lehmann representation, for Green’s functions at zero temperature 66 72—79 107 Lehmann representation, for polarization propagator 117p 174 300—301 559 Lehmann representation, for real-time Green’s function 293—294 Lehmann representation, for temperature Green’s function 297 Lifetime of excitations 81—82 119p 146—147 291 308 309p 310p LIMIT 288—289 293 296 308p Linear response 172—175 Linear response, at finite temperature 298—303 Linear response, electron scattering 188—194 Linear response, in finite nuclei 566 577p Linear response, neutron scattering 196—197p Linear response, of charged Bose gas 501p Linear response, of electron gas 175—183 303—308 Linear response, of superconductor 454—466 Linear response, to weak magnetic field 309p 454—466 477p
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