Lectures on The Many-Body Problems V1
- 1st Edition - December 2, 2012
- Imprint: Academic Press
- Editor: E.R. Caianiello
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 4 3 1 6 4 4 - 7
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 1 5 4 4 7 - 5
Lectures on Field Theory and the Many-Body Problem is a 23-chapter lecture series on the developments in the understanding of the structure and axiomatics of Field Theory, which… Read more
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Request a sales quoteLectures on Field Theory and the Many-Body Problem is a 23-chapter lecture series on the developments in the understanding of the structure and axiomatics of Field Theory, which has proved to be a most useful tool in the study of many-body problems. This book starts with a brief introduction to the TCP theorem, followed by a discussion on the gauge properties of the quantum electrodynamical quantities. The subsequent chapters describe the features and applications of unstable and composite particles to quantum field theory. These topics are followed by significant chapters on other aspects of the field theory, including the configuration space method, Wightman functions, vacuum expectation value, Pais doublets, time reversal in nuclear forces, and symmetry operations in quantum mechanics. This text also covers the ground state theory of many-particle systems and the many body problems at non-zero temperature. The last chapters explore the behavior of a Boson system, the polaron model, and the mathematical aspects of the Hilbert spaces. Physicists and researchers in allied sciences will find this book of great value.
Contributors
Preface
TCP Theorem and Related Problems
I. Connection between Spin and Statistics
II. The TCP Theorem
III. Particles and Antiparticles
References
The Gauge Transformation of Propagators in Quantum Electrodynamics
I. Introduction
II. The Generating Functional
III. Quantum Electrodynamics
IV. Generalized Gauge Transformations
References
Unstable Particles and Complex Poles of the Propagators
I. Introduction
II. The Resolvent and Its Singularities
III. The Exponential Decay
IV. The Representation of Amplitudes
References
Description of Unstable Particles in Quantum Field Theory
I. Introduction
II. Properties of Scattering Amplitudes in the Lee Model
III. Definition of the Unstable V-Particles by Means of the Propagator
IV. Analytical Continuation of the Propagator in a More General Field Theory
V. Remarks on the Time-Graph of an Unstable Particle
References
The Asymptotic Condition and Dispersion Relations
I. Asymptotic Condition. Bound States
II. Reduction Technique and Applications
III. Derivation of Dispersion Relations and Δ2-Analyticity
IV. Results and Possible Causes of Limitations
V. Physical Interpretation of Dispersion Relations. Macrocausality
VI. Dyson's Theorem. High-Energy Behavior
Application of Dispersion Relations to the Determination of Coupling Constants
Second Quantization and Configuration Space Method
I. Configuration Space Wave Functions
II. Algebraic Representation of the State Vectors
III. Dual Space
IV. Linear Operators of ΛR
V. One-Particle Operators
VI. Two-Particle Operators
VII. Field Quantities and Field Equations
Regularization and Renormalization
Properties of Wightman Functions
I. Introduction
II. Some Properties of the Lorentz Group
III. The Theorem of Bargmann, Hall, and Wightman
IV. The Real Regularity Points of R'N and of the Permuted Domain
V. The OTP-Theorem and the Connection between Spin and Statistics
VI. On the Structure of R'N
Appendix to Part IV
References
Analyticity of Vacuum Expectation Values
I. Preface
II. Introduction
III. Simple Illustration of Completion of Analyticity Domains
IV. Reduction of Parameters in the DAÎAD Representation of the M3 Boundary
V. Proof that the M3 Boundary Contains a Non-Analytic Hypersurface
VI. Discussion
References
Connection between Wightman Functions and r -Functions
I. Statement of the Problem
II. The Multiple Commutator
III. The Function r(k1; k2; k3)
IV. The Existence of K
V. Concluding Remarks
References
A Note on the Transformation ψ'= exp [iy5a]ψ
I. Definitions
II. The Mass Theorem
III. Mass and Degeneracy
IV. Application to the Heisenberg Type Theory
V. The Significance of R
References
Pais Doublets and Weak Interactions
Time Reversal in Nuclear Forces
I. Nuclear Reactions (No Polarization)
II. Polarization Measurements
III. Beta-Decay
IV. Correlations in Successive Radiations
References
On Symmetry Operations in Quantum Mechanics
I. Fixing a Quantum Mechanical System
II. Defining Rays, Unit Rays, States, etc
III. Defining Symmetry Operations in Physical Terms
IV. Defining Transformations in Hubert Space Out of Ray Transformations
V. Several Properties of the Transformations θ ~ θ
VI. Proof of the Main Theorem
VII. Representation up to a Factor
Remarks on the Nucleon Form Factors in the Configuration Space
Global Symmetry of the Elementary Particles
I. Fundamental Assumptions
II. β-Decay
References
Ground State Theory of Many-Particle Systems
I. Introduction
II. The Goldstone Approach
III. Resolvent Technique
IV. Difficulties of Perturbation Theory for the Fermi Gas
References
On the Many Body Problem at Non-Zero Temperature
I. Introduction
II. Expansion of the Grand Partition Function
III. The Generalized Theorem of Wick
IV. The Gibbs Potential
V. Further Transformations of the Expansion
VI. A Second Method of Expanding the Grand Partition Function
VII. Relation between the Two Expansions
VIII. The Shielded Potential and the Contribution of the Binary Collisions
References
Collective Behavior of a Boson System
The Theory of Superconductivity
The Polaron Model
I. Introduction
II. Pekar's Product Ansatz
III. Translational Invariance
IV. Adiabatic Approach of Bogoliubov and Tiablikov
V. A Variational Method Connecting the Strong and Weak Coupling Limits
VI. Special Cases of the Variational Ansatz
VII. Influence of a Cutoff
VIII. Final Remarks
References
Free Fields and Multilinear Algebra over Hilbert Spaces
I. Second Quantized Schrödinger Equation
II. Scalar Neutral Field
III. Electron-Positron Field
IV. Photon Field
References
Author Index
Subject Index
- Edition: 1
- Published: December 2, 2012
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9780124316447
- eBook ISBN: 9780323154475
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