Quantum Theory of Many-Particle Systems,9780486428277

Quantum Theory of Many-Particle Systems

by ;
ISBN13: 9780486428277
ISBN10: 0486428273
Format: Paperback
Pub. Date: 2003-06-20
Publisher(s): Dover Publications
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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

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