Quantum Theory of Many-Particle Systems

, by Fetter, Alexander L.; Walecka, John Dirk

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ISBN: 9780486428277 | 0486428273
Cover: Paperback
Copyright: 6/20/2003

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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.

PREFACE TO THE DOVER EDITION

vii

PREFACE

PART ONE INTRODUCTION

(50)

CHAPTER 1 SECOND QUANTIZATION

(30)

1 THE SCHRÖDINGER EQUATION IN FIRST AND SECOND QUANTIZATION

(15)

Bosons

(5)

Many-particle Hilbert space and creation and destruction operators

(3)

Fermions

(4)

2 FIELDS

(2)

3 EXAMPLE: DEGENERATE ELECTRON GAS

(12)

CHAPTER 2 STATISTICAL MECHANICS

(18)

4 REVIEW OF THERMODYNAMICS AND STATISTICAL MECHANICS

(2)

5 IDEALGAS

(17)

Bosons

(7)

Fermions

(6)

PART TWO GROUND-STATE (ZERO-TEMPERATURE) FORMALISM

(174)

CHAPTER 3 GREEN'S FUNCTIONS AND FIELD THEORY (FERMIONS)

(67)

6 PICTURES

(11)

Schrödinger picture

(1)

Interaction picture

(4)

Heisenberg picture

(1)

Adiabatic "switching on"

(2)

Gell-Mann and Low theorem on the ground state in quantum field theory

(3)

7 GREEN'S FUNCTIONS

(19)

Definition

(2)

Relation to observables

(4)

Example : free fermions

(2)

The Lehmann representation

(7)

Physical interpretation of the Green's function

(4)

8 WICK'S THEOREM

(9)

9 DIAGRAMMATIC ANALYSIS OF PERTURBATION THEORY

(28)

Feynman diagrams in coordinate space

(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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Quantum Theory of Many-Particle Systems

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