Quantum Theory of Many-Particle Systems

by Fetter, Alexander L.; Walecka, John Dirk

• ISBN13: 9780486428277
• ISBN10: 0486428273
• Format: Paperback
• Copyright: 2003-06-20
• Publisher: Dover Publications

Summary

This self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to physical systems. 149 figures. 8 tables. 1971 edition.

Table of Contents

PREFACE TO THE DOVER EDITION	vii
PREFACE	ix
PART ONE INTRODUCTION	1	(50)
CHAPTER 1 SECOND QUANTIZATION	3	(30)
1 THE SCHRÖDINGER EQUATION IN FIRST AND SECOND QUANTIZATION	4	(15)
Bosons	7	(5)
Many-particle Hilbert space and creation and destruction operators	12	(3)
Fermions	15	(4)
2 FIELDS	19	(2)
3 EXAMPLE: DEGENERATE ELECTRON GAS	21	(12)
CHAPTER 2 STATISTICAL MECHANICS	33	(18)
4 REVIEW OF THERMODYNAMICS AND STATISTICAL MECHANICS	34	(2)
5 IDEALGAS	36	(17)
Bosons	38	(7)
Fermions	45	(6)
PART TWO GROUND-STATE (ZERO-TEMPERATURE) FORMALISM	51	(174)
CHAPTER 3 GREEN'S FUNCTIONS AND FIELD THEORY (FERMIONS)	53	(67)
6 PICTURES	53	(11)
Schrödinger picture	53	(1)
Interaction picture	54	(4)
Heisenberg picture	58	(1)
Adiabatic "switching on"	59	(2)
Gell-Mann and Low theorem on the ground state in quantum field theory	61	(3)
7 GREEN'S FUNCTIONS	64	(19)
Definition	64	(2)
Relation to observables	66	(4)
Example : free fermions	70	(2)
The Lehmann representation	72	(7)
Physical interpretation of the Green's function	79	(4)
8 WICK'S THEOREM	83	(9)
9 DIAGRAMMATIC ANALYSIS OF PERTURBATION THEORY	92	(28)
Feynman diagrams in coordinate space	92	(8)
Feynman diagrams in momentum space	100	(5)
Dyson's equations	105	(6)
Goldstone's theorem	111	(9)
CHAPTER 4 FERMI SYSTEMS	120	(51)
10 HARTREE-FOLK APPROXIMATION	121	(7)
11 IMPERFECT FERMI GAS	128	(23)
Scattering from a hard sphere	128	(2)
Scattering theory in momentum space	130	(1)
Ladder diagrams and the Bethe-Salpeter equation	131	(8)
Galitskii's integral equations	139	(3)
The proper self-energy	142	(4)
Physical quantities	146	(3)
Justification of terms retained	149	(2)
12 DEGENERATE ELECTRON GAS	151	(20)
Ground-state energy and the dielectric constant	151	(3)
Ring diagrams	154	(4)
Evaluation of II0	158	(5)
Correlation energy	163	(3)
Effective interaction	166	(5)
CHAPTER 5 LINEAR RESPONSE AND COLLECTIVE MODES	171	(27)
13 GENERAL THEORY OF LINEAR RESPONSE TO AN EXTERNAL PERTURBATION	172	(3)
14 SCREENING IN AN ELECTRON GAS	175	(5)
15 PLASMA OSCILLATIONS IN AN ELECTRON GAS	180	(3)
16 ZERO SOUND IN AN IMPERFECT FERMI GAS	183	(5)
17 INELASTIC ELECTRON SCATTERING	188	(10)
CHAPTER 6 BOSS SYSTEMS	198	(27)
18 FORMULATION OF THE PROBLEM	199	(4)
19 GREEN'S FUNCTIONS	203	(4)
20 PERTURBATION THEORY AND FEYNMAN RULES	207	(8)
Interaction picture	207	(1)
Feynman rules in coordinate space	208	(1)
Feynman rules in momentum space	209	(2)
Dyson's equations	211	(3)
Lehmann representation	214	(1)
21 WEAKLY INTERACTING BOSE GAS	215	(3)
22 DILUTE BOSE GAS WITH REPULSIVE CORES	218	(7)
PART THREE FINITE-TEMPERATURE FORMALISM	225	(86)
CHAPTER 7 FIELD THEORY AT FINITE TEMPERATURE	227	(28)
23 TEMPERATURE GREEN'S FUNCTIONS	227	(7)
Definition	228	(1)
Relation to observables	229	(3)
Example: noninteracting system	232	(2)
24 PERTURBATION THEORY AND WICK'S THEOREM FOR FINITE TEMPERATURES	234	(7)
Interaction picture	234	(2)
Periodicity of	236	(1)
Proof of Wick's theorem	237	(4)
25 DIAGRAMMATIC ANALYSIS	241	(9)
Feynman rules in coordinate space	242	(2)
Feynman rules in momentum space	244	(4)
Evaluation of frequency sums	248	(2)
26 DYSON'S EQUATIONS	250	(5)
CHAPTER 8 PHYSICAL SYSTEMS AT FINITE TEMPERATURE	255	(36)
27 HARTREE-FOCK APPROXIMATION	255	(4)
28 IMPERFECT BOSE GAS NEAR Tc	259	(2)
29 SPECIFIC HEAT OF AN IMPERFECT FERMI GAS AT LOW TEMPERATURE	261	(6)
Low-temperature expansion of	262	(1)
Hartree-Fock approximation	262	(3)
Evaluation of the entropy	265	(2)
30 ELECTRON GAS	267	(24)
Approximate proper self-energy	268	(3)
Summation of ring diagrams	271	(2)
Approximate thermodynamic potential	273	(2)
Classical limit	275	(6)
Zero-temperature limit	281	(10)
CHAPTER 9 REAL-TIME GREEN'S FUNCTIONS AND LINEAR RESPONSE	291	(20)
31 GENERALIZED LEHMANN REPRESENTATION	292	(6)
Definition of G	292	(2)
Retarded and advanced functions	294	(3)
Temperature Green's functions and analytic continuation	297	(1)
32 LINEAR RESPONSE AT FINITE TEMPERATURE	298	(5)
General theory	298	(2)
Density correlation function	300	(3)
33 SCREENING IN AN ELECTRON GAS	303	(4)
34 PLASMA OSCILLATIONS IN AN ELECTRON GAS	307	(4)
PART FOUR CANONICAL TRANSFORMATIONS	311	(28)
CHAPTER 10 CANONICAL TRANSFORMATIONS	313	(26)
35 INTERACTING BOSE GAS	314	(6)
36 COOPER PAIRS	320	(6)
37 INTERACTING FERMI GAS	326	(13)
PART FIVE APPLICATIONS TO PHYSICAL SYSTEMS	339	(240)
CHAPTER 11 NUCLEAR MATTER	341	(48)
38 NUCLEAR FORCES: A REVIEW	341	(7)
39 NUCLEAR MATTER	348	(4)
Nuclear radii and charge distributions	348	(1)
The semiempirical mass formula	349	(3)
40 INDEPENDENT-PARTICLE (FERMI-GAS) MODEL	352	(5)
41 INDEPENDENT-PAIR APPROXIMATION (BRUECKNER'S THEORY)	357	(20)
Self-consistent Bethe-Goldstone equation	358	(2)
Solution for a nonsingular square-well potential	360	(3)
Solution for a pure hard-core potential	363	(3)
Properties of nuclear matter with a "realistic" potential	366	(11)
42 RELATION TO GREEN'S FUNCTIONS AND BETHS-SALPETER EQUATION	377	(6)
43 THE ENERGY GAP IN NUCLEAR MATTER	383	(6)
CHAPTER 12 PHONONS AND ELECTRONS	389	(24)
44 THE NONINTERACTING PHONON SYSTEM	390	(6)
Lagrangian and hamiltonian	391	(2)
Debye theory of the specific heat	393	(3)
45 THE ELECTRON-PHONON INTERACTION	396	(3)
46 THE COUPLED-FIELD THEORY	399	(7)
Feynman rules for T = 0	399	(2)
The equivalent electron-electron interaction	401	(1)
Vertex parts and Dyson's equations	402	(4)
47 MIGDAL'S THEOREM	406	(7)
CHAPTER 13 SUPERCONDUCTIVITY	413	(66)
48 FUNDAMENTAL PROPERTIES OF SUPERCONDUCTORS	414	(6)
Basic experimental facts	414	(3)
Thermodynamic relations	417	(3)
49 LONDON-PIPPARD PHENOMENOLOGICAL THEORY	420	(10)
Derivation of London equations	420	(1)
Solution for halfspace and slab	421	(2)
Conservation and quantization of fluxoid	423	(2)
Pippard's generalized equation	425	(5)
50 GINZBURG-LANDAU PHENOMENOLOGICAL THEORY	430	(9)
Expansion of the free energy	430	(2)
Solution in simple cases	432	(3)
Flux quantization	435	(1)
Surface energy	436	(3)
51 MICROSCOPIC (BCS) THEORY	439	(15)
General formulation	439	(5)
Solution for uniform medium	444	(3)
Determination of the gap function LX(T)	447	(2)
Thermodynamic functions	449	(5)
52 LINEAR RESPONSE TO A WEAK MAGNETIC FIELD	454	(12)
Derivation of the general kernel	455	(4)
Meissner effect	459	(2)
Penetration depth in Pippard (nonfocal) limit	461	(2)
Nonfocal integral relation	463	(3)
53 MICROSCOPIC DERIVATION OF GINZBURG-LANDAU EQUATIONS	466	(13)
CHAPTER 14 SUPERFLUID HELIUM	479	(24)
54 FUNDAMENTAL PROPERTIES OF He 11	481	(7)
Basic experimental facts	481	(3)
Landau's quasiparticle model	484	(4)
55 WEAKLY INTERACTING BOSE GAS	488	(15)
General formulation	489	(3)
Uniform condensate	492	(3)
Nonuniform condensate	495	(8)
CHAPTER 15 APPLICATIONS TO FINITE SYSTEMS: THE ATOMIC NUCLEUS	503	(76)
56 GENERAL CANONICAL TRANSFORMATION TO PARTICLES AND HOLES	504	(4)
57 THE SINGLE-PARTICLE SHELL MODEL	508	(7)
Approximate Hartree-Fock wave functions and level orderings in a central potential	508	(3)
Spin-orbit splitting	511	(1)
Single-particle matrix elements	512	(3)
58 MANY PARTICLES IN A SHELL	515	(23)
Two valence particles: general interaction and 6(x) force	515	(4)
Several particles: normal coupling	519	(4)
The pairing-force problem	523	(3)
The boson approximation	526	(1)
The Bogoliubov transformation	527	(11)
59 EXCITED STATES: LINEARIZATION OF THE EQUATIONS OF MOTION	538	(20)
Tamm-Dancoff approximation (TDA)	538	(2)
Random-phase approximation (RPA)	540	(3)
Reduction of the basis	543	(4)
Solution for the [15]-dimensional supermultiplet with a 8(x) force	547	(8)
An application to nuclei : 016	555	(3)
60 EXCITED STATES: GREEN'S FUNCTION METHODS	558	(9)
The polarization propagator	558	(6)
Random-phase approximation	564	(1)
Tamm-Dancoff approximation	565	(1)
Construction of H(c) in the RPA	566	(1)
61 REALISTIC NUCLEAR FORCES	567	(14)
Two nucleons outside closed shells: the independent-pair approximation	567	(1)
Bethe-Goldstone equation	568	(2)
Harmonic-oscillator approximation	570	(4)
Pauli principle correction	574	(1)
Extensions and calculations of other quantities	574	(5)
APPENDIXES	579	(10)
A DEFINITE INTEGRALS	579	(2)
B REVIEW OF THE THEORY OF ANGULAR MOMENTUM	581	(8)
Basic commutation relations	581	(1)
Coupling of two angular momenta:Clebsch-Gordan coefficients	582	(3)
Coupling of three angular momenta:the 6-j coefficients	585	(1)
Irreducible tensor operators and the aligner-Eckart theorem	586	(1)
Tensor operators in coupled schemes	587	(2)
INDEX	589