Quantum Many-particle Systems

✍ Scribed by John W. Negele, Henri Orland

• Publisher: Westview Press
• Year: 1998
• Tongue: English
• Leaves: 474
• Series: Advanced Book Classics
• Category: Library

✦ Synopsis

This volume explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonpurturbative approximations based on functional integrals; general arguments based on order parameters; symmetry, and Fermi liquid theory; and stochastic methods. Each approach provides its own insights and quantitative capabilities, and in conjunction provide a powerful framework for understanding a wide variety of physical systems. Written at a level for graduate students with no prior background in manybody theory, this classic text is intended for physicists in solid state physics, field theory, atomic physics, condensed matter physics, quantum chemistry, and nuclear physics.

✦ Table of Contents

Contents......Page 12
1.1 Quantum Mechanics of a Single Particle......Page 16
1.2 Systems of Identical Particles......Page 19
1.3 Many-Body Operators......Page 24
1.4 Creation and Annihilation Operators......Page 26
Boson Coherent States......Page 35
Grassmann Algebra......Page 40
Fermion Coherent States......Page 44
Gaussian Integrals......Page 48
Problems for Chapter 1......Page 52
Quantum Statistical Mechanics......Page 62
Physical Response Functions and Green's Functions......Page 64
Approximation Strategies......Page 68
Feynman Path Integral......Page 72
Imaginary-Time Path Integral and the Partition Function......Page 78
Coherent State Functional Integral......Page 81
The Partition Function for Many-Particle Systems......Page 83
2.3 Perturbation Theory......Page 89
Wick's Theorem......Page 90
Labeled Feynman Diagrams......Page 93
Unlabeled Feynman Diagrams......Page 97
Hugenholtz Diagrams......Page 103
Frequency and Momentum Representation......Page 107
The Linked Cluster Theorem......Page 111
Calculation of Observables and Green's functions......Page 112
Generating Function for Connected Green's Functions......Page 120
The Effective Potential......Page 123
The Self-Energy and Dyson's Equation......Page 126
Higher-Order Vertex Functions......Page 130
2.5 Stationary-Phase Approximation and Loop Expansion......Page 135
One-Dimensional Integral......Page 136
Feynman Path Integral......Page 138
Many-Particle Partition Function......Page 139
Problems for Chapter 2......Page 146
Observables......Page 153
Zero-Temperature Fermion Propagators......Page 157
Fermion Diagram Rules......Page 161
Bosons......Page 168
3.2 Time-Ordered Diagrams......Page 172
3.3 The Zero-Temperature Limit......Page 179
Problems for Chapter 3......Page 182
Phases of Two Familiar Systems......Page 191
Phenomenological Landau Theory......Page 194
Broken Symmetry......Page 199
Infinite Range Ising Model......Page 200
Generalizations......Page 205
Physical Examples......Page 207
Legendre Transform......Page 210
Ferromagnetic Transition for Classical Spins......Page 212
Application to General Systems......Page 219
Landau Ginzburg Theory and Dimensional Analysis......Page 222
One-Loop Corrections......Page 226
Continuous Symmetry......Page 229
One-Loop Corrections for the x – y model......Page 232
Lower Critical Dimension......Page 235
The Anderson-Higgs Mechanism......Page 237
Problems for Chapter 4......Page 241
Definitions......Page 250
Evaluation of Observables......Page 252
Zero Temperature Green's Functions......Page 255
Finite Temperature Green's Functions......Page 259
5.3 Physical Content of the Self Energy......Page 264
Quasiparticle Pole......Page 266
Effective Masses......Page 270
Optical Potential......Page 274
The Response Function......Page 277
Random Phase Approximation......Page 280
Zero Sound......Page 286
Matrix Form of RPA......Page 291
Sum Rules and Examples......Page 292
Static Susceptibility at Zero Temperature......Page 296
Static Susceptibility at Finite Temperature......Page 297
Dynamic Susceptibility at Finite Temperature......Page 299
Problems for Chapter 5......Page 300
6.1 Quasiparticles and their Interactions......Page 311
Equilibrium Properties......Page 314
Nonequilibrium Properties and Collective Modes......Page 320
6.3 Microscopic Foundation......Page 328
Calculation of the Quasiparticle Interaction......Page 337
Problems for Chapter 6......Page 339
The Auxiliary Field......Page 347
Overcomplete Sets of States......Page 351
The Resolvent Operator......Page 355
Static Hartree Approximation......Page 357
RPA Corrections......Page 359
The Loop Expansion......Page 363
7.3 Transition Amplitudes......Page 365
S-Matrix Elements......Page 367
7.4 Collective Excitations and Tunneling......Page 368
Example of One Degree of Freedom......Page 369
Eigenstates of Large Amplitude Collective Motion......Page 375
Barrier Penetration and Spontaneous Fission......Page 379
Conceptual Questions......Page 385
7.5 Large Orders of Perturbation Theory......Page 386
Study of a Simple Integral......Page 387
Borel Summation......Page 388
The Anharmonic Oscillator......Page 391
Problems for Chapter 7......Page 397
8.1 Monte Carlo Evaluation of Integrals......Page 415
Central Limit Theorem......Page 416
Importance Sampling......Page 418
Sampling Simple Functions......Page 421
Markov Processes......Page 423
Neumann-Ulam Matrix lnversion......Page 427
Microcanonical Methods......Page 428
Observables......Page 431
Sampling the Action......Page 432
Initial Value Random Walk......Page 434
Tunneling......Page 438
Path Integral in Coordinate Representation......Page 441
Functional Integrals Over Fields......Page 446
8.5 Spin Systems and Lattice Fermions......Page 449
Checkerboard Decomposition......Page 450
Special Methods for Spins......Page 453
Problems for Chapter 8......Page 455
References......Page 462
E......Page 470
H......Page 471
P......Page 472
S......Page 473
Z......Page 474