
Quantum Many-Body Physics in a Nutshell
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The ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates
This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields-phenomena as well as theoretical tools-and does so in a simple and accessible way.
Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle; in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses, and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid ³He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of quantized vortices in superfluids and superconductors to ensembles of colored (QCD) monopoles and instantons in the QCD vacuum.
Proven in the classroom, Quantum Many-Body Physics in a Nutshell is the ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates.
- Teaches students how quantum many-body systems work across many fields of physics
- Uses path integrals from the very beginning
- Features the easiest introduction to Feynman diagrams available
- Draws on the most recent findings, including trapped Fermi and Bose atomic gases
- Guides students from traditional systems, such as electron gas and nuclear matter, to more advanced ones, such as quark-gluon plasma and the QCD vacuum
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Content
- Cover
- Title
- Copyright
- Contents
- Preface
- 1 Introduction
- 1.1 Prerequisites and Textbooks
- 1.2 Physical Phenomena and Theoretical Tools
- 1.3 Feynman's Path Integrals
- 1.4 Quantum Statistical Mechanics of a Particle
- 1.5 A Few Gaussian Integrals
- 1.6 Another Take on the Path Integral for the Harmonic Oscillator
- 2 Feynman Diagrams in Quantum/Statistical Mechanics
- 2.1 Anharmonic Oscillators à la Quantum Mechanics Textbooks
- 2.2 The First Feynman Diagrams
- 2.3 Disconnected Diagrams
- 2.4 Diagrams in ? Representation and Their Resummation
- 3 Real Scalar Fields and the Renormalization Group
- 3.1 Path Integrals for a Scalar Field
- 3.2 Matsubara Sums Lead to the Particle/Hole Interpretation of the Diagrams
- 3.3 Weakly Interacting Scalar Field
- 3.4 Symmetry Breaking and the Landau Theory of Second-Order Phase Transitions
- 3.5 More on Critical Indices
- 3.6 Renormalization Group and Wilson's Epsilon-Expansion
- 4 Complex Scalar Fields
- 4.1 Phase Symmetry and Its Breaking
- 4.2 Conserved Charge and the Chemical Potential
- 4.3 Nonrelativistic Approximation and Normalization
- 4.4 Weakly Coupled Bose Gas and Bose-Einstein Condensation
- 4.5 Renormalized Quasiparticles and Condensates
- 4.6 Summary of Perturbation Theory for a Weakly Coupled Bose Gas
- 5 Liquid 4He
- 5.1 History
- 5.2 Superfluidity in Experiments
- 5.3 Elementary Excitations
- 5.4 Quasiparticle Decays in a Weakly Coupled Bose Gas and in He-II
- 5.5 Landau's Criterion for Superfluidity
- 5.6 Rotation and Vortices
- 6 Bose-Einstein Condensation of Trapped Ultracold Atoms
- 6.1 History of BEC
- 6.2 Depletion of the Condensate
- 6.3 Gross-Pitaevsky Equation and Repulsive/Attractive Bose Gas
- 6.4 Rotation
- 7 The Electron Gas
- 7.1 Fermi Systems Discussed in This Book
- 7.2 Path Integrals and Matsubara Sums for Fermions
- 7.3 Weakly Interacting Fermi Gas
- 7.4 Cold Electron Gas
- 7.5 The Polarization Diagram and the Lindhard Function
- 7.6 The Strongly Coupled Electron Fluid in Graphene
- 8 Nuclear Matter
- 8.1 Nuclear Forces
- 8.2 Nuclear Matter in the Relativistic Mean-Field Model
- 8.3 Nuclear Forces and RG
- 8.4 Nuclear Matter and RG
- 8.5 Relativistic Mean Field and the Optical Potential
- 9 Cooper Pairing and the BCS Theory of Superconductivity
- 9.1 Superconducting Metals
- 9.2 Cooper Pairing
- 9.3 A Continuous RG
- 9.4 RG and Cold Fermi Systems
- 9.5 BCS Pairing and Gorkov's Anomalous Green Functions
- 10 Pairing in Liquid 3He and in Nuclear Matter
- 10.1 Liquid 3He and Landau's Fermi Liquids
- 10.2 Zero Sound and the Peierls Instability from the Resummed Lindhard Diagram
- 10.3 Superfluidity in 3He
- 10.4 Pairing in Nuclei and Nuclear Matter
- 11 Vortices and Topological Matter
- 11.1 The BKT Phase Transition of Vortex Matter in Two Dimensions
- 11.2 Vortices in Superconductors
- 11.3 Type I and II Superconductors
- 11.4 Phase Transitions in Strongly Rotating Nuclei
- 11.5 Glitches of Pulsars
- 12 Strongly Coupled Fermionic Gases
- 12.1 Weak and Strong Coupling Regimes in Trapped Fermionic Gases
- 12.2 Global Phase Diagram
- 12.3 Thermodynamics and Kinetics at Strong Coupling
- 13 Numerical Evaluation of Path Integrals
- 13.1 Numerical Evaluation of Multidimensional Integrals
- 13.2 First Steps: The Path-Integral Monte Carlo Method for Few-Body Systems with Distinguishable Particles
- 13.3 Liquid 4He PIMC Simulations: Bose Clusters, Condensation, and the Critical Temperature
- 13.4 Path Integrals for Fermions
- 14 Quantum Field Theories on the Lattice and Supercomputers
- 14.1 History
- 14.2 Gauge-Invariant Abelian Theory on the Lattice
- 14.3 Non-Abelian Gauge Theory on the Lattice
- 15 Theory of Quark-Gluon Plasma
- 15.1 Overview and Scales of Quark-Gluon Plasmas
- 15.2 The Perturbative Formalism of QCD
- 15.3 The Polarization Operator
- 15.4 Cold Quark Matter and Perturbation Theory
- 15.5 Ring Diagram Resummation
- 15.6 IR Divergences and Magnetic Sector
- 15.7 Where Do the Perturbative Series Converge?
- 15.8 Hard Thermal Loop Resummations and the Quasiparticle Gas
- 15.9 Lattice Gauge Theory Simulations at Finite Temperature
- 16 Quark-Gluon Plasma in Experiment
- 16.1 Experimental Quest for QGP
- 16.2 Mapping the Phase Diagram
- 16.3 Collective Flow and Viscosity of QGP
- 16.4 Relativistic Hydrodynamics
- 16.5 The Little Bang versus the Big Bang: Sound Circles and Fluctuations
- 16.6 Phase Transitions in the Big Bang: Sound Cascades and Gravitational Waves
- 17 The QCD Vacuum I. Monopoles and Confinement
- 17.1 Confinement and Flux Tubes
- 17.2 Monopoles in Non-Abelian Theories
- 17.3 Electric-Magnetic Duality and RG Flow
- 17.4 Strongly Coupled QGP as a "Dual" Plasma
- 18 The QCD Vacuum II. Chiral Symmetries and Their Breaking
- 18.1 Light Quarks and Chiral Symmetries
- 18.2 The (Nonexistent) Ua(1) Chiral Symmetry
- 18.3 The Nambu-Jona-Lasinio Model
- 18.4 Gauge Topology and Chiral Symmetry Breaking
- 19 Chiral Matter
- 19.1 Electrodynamics in CP-Violating Matter
- 19.2 Chiral Magnetic Effect
- 19.3 Chiral Vortical Effect
- 19.4 Chiral Waves
- 20 Cold Quark Matter and Color Superconductivity
- 20.1 Quark Cooper Pairs
- 20.2 Topology-Induced Color Superconductivity: The 2SC Phase
- 20.3 Three-Flavor QCD: The Color-Flavor-Locked Phase
- 20.4 Magnetic Pairing in Asymptotically Dense Matter
- 21 The QCD Vacuum III: Instanton-Dyons
- 21.1 Nonzero Holonomy and Finite-Temperature "Higgsing"
- 21.2 Instanton-Dyons and Their Ensembles
- 21.3 Modifying Quark Periodicity in Euclidean Time
- 22 Parting Comments
- 22.1 Feynman Diagrams and Their Resummations
- 22.2 Bose-Einstein Condensation and the Reality of Cooper Pairs
- 22.3 Pairing Can Occur Even without the Fermi Surface!
- 22.4 Topological Matter
- 22.5 RG Flows and Dualities
- References
- Index
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