Many-body problems and quantum field theory : an introduction /
Saved in:
| Author / Creator: | Martin, Philippe A. |
|---|---|
| Uniform title: | Problèmes à N-corps et champs quantiques. English |
| Imprint: | Berlin ; New York : Springer, c2002. |
| Description: | xiii, 441 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Texts and monographs in physics, 0172-5998 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4592308 |
Table of Contents:
- 1. Classical Fields and Their Associated Particles
- 1.1. Introduction
- 1.2. The Quantum Harmonic Oscillator
- 1.2.1. Review of Properties
- 1.2.2. Coherent States
- 1.2.3. The Forced Oscillator
- 1.2.4. Normal Order
- 1.3. The Electromagnetic Field and the Photon
- 1.3.1. Maxwell's Equations
- 1.3.2. Gauge Transformations
- 1.3.3. Decomposition of the Field into Longitudinal and Transverse Components
- 1.3.4. Hamiltonian of the Interaction of Radiation with Non-Relativistic Matter
- 1.3.5. Fourier Analysis of the Classical Free Field
- 1.3.6. Photons and Electromagnetic Waves
- 1.4. The Elastic Field and the Phonon
- 1.4.1. Elastic Waves and Elastic Energy
- 1.4.2. Elastic Waves and Energy of an Isotropic Solid
- 1.4.3. Fourier Analysis of Elastic Waves
- 1.4.4. An Ensemble of Phonons and Classical Elastic Waves
- 1.4.5. The Classical Linear Chain
- 1.4.6. The Linear Quantum Chain
- Exercises
- 2. Fermions and Bosons
- 2.1. The Principle of Symmetrization
- 2.1.1. Identical Particles
- 2.1.2. One-Particle States
- 2.1.3. Periodic Boundary Conditions and the Thermodynamic Limit
- 2.1.4. n-Particle States
- 2.1.5. Symmetrization
- 2.1.6. Symmetry of Composite Particles
- 2.1.7. Occupation Number Representation
- 2.2. Degenerate Gases
- 2.2.1. The Ground State of n Bosons
- 2.2.2. The Ground State of n Fermions
- 2.2.3. Stability of Matter
- 2.2.4. Nucleo-Electronic Plasma at High Density
- 2.2.5. Fermions and Gravitation
- Exercises
- 3. Systems with Variable Particle Number
- 3.1. Introduction
- 3.2. Formalism of the Second Quantization
- 3.2.1. Fock Space
- 3.2.2. Creation and Annihilation Operators
- 3.2.3. States of Fock Space
- 3.2.4. Normal Order
- 3.2.5. One-Body Operators
- 3.2.6. Free Evolution and Symmetries
- 3.2.7. Two-Body Operators
- 3.2.8. Reduced Density Matrices and Correlations
- 3.2.9. Correlations in Free Fermi and Bose Gases
- 3.3. Quantum Physics and the Concept of a Perfect Gas
- Exercises
- 4. Electron Gas
- 4.1. The Hartree-Fock Method
- 4.1.1. The Variational Principle
- 4.1.2. The Hartree-Fock Equations
- 4.2. Electron Gas in the Hartree-Fock Approximation
- 4.2.1. Electron Gas and Its Hamiltonian
- 4.2.2. The Hartree-Fock Energy
- 4.3. The Dielectric Function
- 4.3.1. Screening and the Plasmon
- 4.3.2. Response to an External Charge
- 4.3.3. Evolution of a Charge Fluctuation
- 4.3.4. The RPA Dielectric Function
- Exercises
- 5. Fermion Pairing and Superconductivity
- 5.1. Does There Exist an Analogue of the Bose Condensation for Fermions?
- 5.2. The Phenomenology of Superconductivity
- 5.2.1. Experimental Facts
- 5.2.2. The Phenomenological Approach
- 5.2.3. Macroscopic Quantum Fluids
- 5.2.4. Existence of the Energy Gap
- 5.3. BCS Theory
- 5.3.1. The Effective Interaction Between Electrons
- 5.3.2. Application of the Variational Method to Superconductivity
- 5.3.3. Sign Ambiguity
- 5.3.4. Variational Class of BCS States
- 5.3.5. How to Calculate with a BCS State
- 5.3.6. Search for a Minimum-Energy State
- 5.3.7. The Energy Gap
- 5.3.8. Spatial Extension of a Cooper Pair
- 5.4. Particle Number and Phase in Superconductivity
- 5.4.1. Is it Necessary to Fix the Particle Number or the Phase?
- 5.4.2. Analogy with Statistical Physics
- 5.5. High-Tc Superconductivity
- Exercises
- 6. Nucleon Pairing and the Structure of the Nucleus
- 6.1. Introduction
- 6.2. A Broad Outline of the Nuclear Structure
- 6.2.1. Nuclear Forces
- 6.2.2. The Liquid Drop Model
- 6.2.3. Pairing Energy
- 6.2.4. Shell Energy
- 6.3. The Shell Model
- 6.3.1. The Average Potential of the Shell Model
- 6.3.2. Magic Numbers
- 6.4. Pairing of the Nucleons
- 6.4.1. Necessity of the Model
- 6.4.2. The Interaction Responsible for the Pairing
- 6.4.3. The Variational Method and the State of Paired Nucleons
- 6.4.4. Determination of the Ground State of a Paired Nucleus
- 6.4.5. Ground and Excited States of a Spherical Paired Nucleus
- 6.4.6. The Spectra of Paired Nuclei
- 6.4.7. Total Angular Momentum of Spherical Even-Even Nuclei
- 6.5. Relation Between Pairing and Superfluidity
- 6.5.1. How Can a Nucleus Be a Superfluid?
- 6.5.2. An Excited Nucleus in a Rotational State
- 6.5.3. Moment of Inertia of a Deformed Nucleus
- Exercises
- 7. The Superfluidity of Liquid Helium
- 7.1. Experimental Facts
- 7.1.1. Phase Diagram of 42He
- 7.1.2. Properties of the Superfluid Phase of He II
- 7.2. Quantum Liquid and the Two-Fluid Model
- 7.2.1. The Superfluid Phase and Quantum Liquid
- 7.2.2. Dissipation in a Superfluid
- 7.2.3. Second Sound
- 7.3. The Energy Spectrum of He II
- 7.3.1. Excitations of He II
- 7.3.2. Non-Viscous Flow Through a Capillary
- 7.4. Imperfect Bose Gas
- 7.4.1. Bogolioubov's Approximation and Transformation
- 7.4.2. Bose Gas or Liquid?
- 7.5. Superfluidity of the Light Isotope 3He
- 7.5.1. A Fermi Liquid
- 7.5.2. Superfluidity of 3He
- Exercises
- 8. Quantum Fields
- 8.1. Introduction
- 8.2. The Quantum-Electromagnetic Field
- 8.2.1. The Free Field
- 8.2.2. Canonical Variables
- 8.2.3. Invariant Commutation Function and Microcausality
- 8.2.4. Emission of Photons by a Classical Source
- 8.2.5. Coherent States of Photons
- 8.2.6. Emission and Absorption of Photons by an Atom
- 8.2.7. Spontaneous Emission
- 8.2.8. Equilibrium of Photons and Matter
- 8.2.9. Photon Statistics
- 8.3. Massive Scalar Field
- 8.3.1. Neutral Scalar Field
- 8.3.2. The Yukawa Potential
- 8.3.3. Charged Scalar Field
- 8.3.4. Spin and Statistics
- 8.3.5. The Lagrangian Formalism
- 8.3.6. The Gauge Invariance Principle and Field Interactions
- 8.3.7. Mass Generation
- 8.4. Electrons and Phonons
- 8.4.1. Non-Relativistic Fermi Field
- 8.4.2. The Quantum-Elastic Field
- 8.4.3. Electron-Phonon Interactions
- Exercises
- 9. Perturbative Methods in Field Theory
- 9.1. Introduction
- 9.2. The Green Functions
- 9.2.1. Definition
- 9.2.2. The Free-Particle Green Function
- 9.2.3. Particle in an External Field
- 9.2.4. Simplified Example: The Cooper Pair
- 9.3. Perturbative Expansion of the Scattering Operator
- 9.3.1. Time-Dependent Perturbation Theory
- 9.3.2. The Scattering Operator
- 9.3.3. Fermions and Bosons in Interaction
- 9.3.4. The Wick Theorem for Chronological Products
- 9.3.5. Chronological Contractions and Propagators
- 9.3.6. Feynman Diagrams
- 9.4. Applications
- 9.4.1. Physical Interpretation of the Diagrams
- 9.4.2. Electromagnetic Interactions: Compton Scattering
- 9.4.3. Quantum Electrodynamics: Radiative Corrections
- 9.4.4. Electron-Phonon Interactions
- 9.4.5. Diagram Summation
- Exercises
- 10. Perturbative Methods in Many-Body Problems
- 10.1. General Properties
- 10.1.1. The One-Body Green Function
- 10.1.2. Perturbative Calculation of the Green Function
- 10.1.3. Particle in an External Field and the Connected-Graph Theorem
- 10.1.4. Particles in Interaction
- 10.2. Approximation Schemes for the Electron Gas
- 10.2.1. Hartree-Fock Approximation
- 10.2.2. RPA Approximation
- Exercises
- Bibliography
- Index
