Format:
1 Online-Ressource (xiv, 459 Seiten)
,
Diagramme
ISBN:
9780429497926
,
9780429966477
Series Statement:
Advanced Books Classics
Content:
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Editorâs Foreword -- PREFACE -- Table of Contents -- Chapter 1: Second Quantization and Coherent States -- 1.1 Quantum Mechanics of a Single Particle -- 1.2 Systems of Identical Particles -- 1.3 Many-Body Operators -- 1.4 Creation and Annihilation Operators -- 1.5 Coherent States -- Boson Coherent States -- Grassmann Algebra -- Fermion Coherent States -- Gaussian Integrals -- Problems for Chapter 1 -- Chapter 2: General Formalism at Finite Temperature -- 2.1 Introduction -- Quantum Statistical Mechanics -- Physical Response Functions and Greenâs Functions -- Approximation Strategies -- 2.2 Functional Integral Formulation -- Feynman Path Integral -- Imaginary-Time Path Integral and the Partition Function -- Coherent State Functional Integral -- The Partition Function for Many-Particle Systems -- 2.3 Perturbation Theory -- Wick's Theorem -- Labeled Feynman Diagrams -- Unlabeled Feynman Diagrams -- Hugenholtz Diagrams -- Frequency and Momentum Representation -- The Linked Cluster Theorem -- Calculation of Observables and Greenâs functions -- 2.4 Irreducible Diagrams and Integral Equations -- Generating Function for Connected Green's Functions -- The EfFective Potential -- The Self-Energy and Dysonâs Equation -- Higher-Order Vertex Functions -- 2.5 Stationary-Phase Approximation and Loop Expansion -- One-Dimensional Integral -- Feynman Path Integral -- Many-Particle Partition Function -- Problems for Chapter 2 -- Chapter 3: Perturbation Theory at Zero Temperature -- 3.1 Feynman Diagrams -- Observables -- Zero-Temperature Fermion Propagators -- Fermion Diagram Rules -- Bosons -- 3.2 Time-Ordered Diagrams -- 3.3 The Zero-Temperature Limit -- Problems for Chapter 3 -- Chapter 4: Order Parameters and Broken Symmetry -- 4.1 Introduction -- Phases of Two Familiar Systems
Content:
Phenomenological Landau Theory -- Broken Symmetry -- 4.2 General Formulation with Order Parameters -- Infinite Range Ising Model -- Generalizations -- Physical Examples -- 4.3 Mean Field Theory -- Legendre Transform -- Ferromagnetic Transition for Classical Spins -- Application to General Systems -- 4.4 Fluctuations -- Landau Ginzburg Theory and Dimensional Analysis -- One-Loop Corrections -- Continuous Symmetry -- One-Loop Corrections for the x - y model -- Lower Critical Dimension -- The Anderson-Higgs Mechanism -- Problems for Chapter 4 -- Chapter 5: Greenâs Functions -- 5.1 Introduction -- Definitions -- Evaluation of Observables -- 5.2 Analytic Properties -- Zero Temperature Greenâs Functions -- Finite Temperature Greenâs Functions -- 5.3 Physical Content of the Self Energy -- Quasiparticle Pole -- Effective Masses -- Optical Potential -- 5.4 Linear Response -- The Response Function -- Random Phase Approximation -- Zero Sound -- Matrix Form of RPA -- Sum Rules and Examples -- 5.5 Magnetic Susceptibility of a Fermi Gas -- Static Susceptibility at Zero Temperature -- Static Susceptibility at Finite Temperature -- Dynamic Susceptibility at Zero Temperature -- Dynamic Susceptibility at Finite Temperature -- Problems for Chapter 5 -- Chapter 6: The Landau Theory of Fermi Liquids -- 6.1 Quasiparticles and their Interactions -- 6.2 Observable Properties of a Normal Fermi Liquid -- Equilibrium Properties -- Nonequilibrium Properties and Collective Modes -- 6.3 Microscopic Foundation -- Calculation of the Quasiparticle Interaction -- Problems for Chapter 6 -- Chapter 7: Further Development of Functional Integrals -- 7.1 Representations of the Evolution Operator -- The Auxiliary Field -- Overcomplete Sets of States -- 7.2 Ground State Properties for Finite Systems -- The Resolvent Operator -- Static Hartree Approximation -- RPA Corrections
Content:
The Loop Expansion -- 7.3 Transition Amplitudes -- S-Matrix Elements -- 7.4 Collective Excitations and Tunneling -- Example of One Degree of Freedom -- Eigenstates of Large Amplitude Collective Motion -- Barrier Penetration and Spontaneous Fission -- Conceptual Questions -- 7.5 Large Orders of Perturbation Theory -- Study of a Simple Integral -- Borel Summation -- The Anharmonic Oscillator -- Problems for Chapter 7 -- Chapter 8: Stochastic Methods -- 8.1 Monte Carlo Evaluation of Integrals -- Central Limit Theorem -- Importance Sampling -- 8.2 Sampling Techniques -- Sampling Simple Functions -- Markov Process -- Neumann-Ulam Matrix Inversion -- Microcanonical Methods -- 8.3 Evaluation of One-Particle Path Integral -- Observables -- Sampling the Action -- Initial Value Random Walk -- Tunneling -- 8.4 Many Particle Systems -- Path Integral in Coordinate Representation -- Functional Integrals Over Fields -- 8.5 Spin Systems and Lattice Fermions -- Checkerboard Decomposition -- Special Methods for Spins -- Problems for Chapter 8 -- References -- Index
Additional Edition:
9780738200521
Additional Edition:
Erscheint auch als Druck-Ausgabe Negele, John W. Quantum many-particle systems Boulder, Colo. [u.a.] : Westview Press, a member of the Perseus Books Group, 1998 0738200522
Language:
English
Subjects:
Physics
Keywords:
Electronic books
DOI:
10.1201/9780429497926
