Lectures on The Many-Body Problems V1

Lectures on The Many-Body Problems V1

1st Edition - January 1, 1962

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  • Editor: E.R. Caianiello
  • eBook ISBN: 9780323154475

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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 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.

Table of Contents

  • Contributors


    TCP Theorem and Related Problems

    I. Connection between Spin and Statistics

    II. The TCP Theorem

    III. Particles and Antiparticles


    The Gauge Transformation of Propagators in Quantum Electrodynamics

    I. Introduction

    II. The Generating Functional

    III. Quantum Electrodynamics

    IV. Generalized Gauge Transformations


    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


    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


    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


    Analyticity of Vacuum Expectation Values

    I. Preface

    II. Introduction

    III. Simple Illustration of Completion of Analyticity Domains

    IV. Reduction of Parameters in the DAΝAD Representation of the M3 Boundary

    V. Proof that the M3 Boundary Contains a Non-Analytic Hypersurface

    VI. Discussion


    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


    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


    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


    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


    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


    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


    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


    Free Fields and Multilinear Algebra over Hilbert Spaces

    I. Second Quantized Schrödinger Equation

    II. Scalar Neutral Field

    III. Electron-Positron Field

    IV. Photon Field


    Author Index

    Subject Index

Product details

  • No. of pages: 356
  • Language: English
  • Copyright: © Academic Press 1962
  • Published: January 1, 1962
  • Imprint: Academic Press
  • eBook ISBN: 9780323154475

About the Editor

E.R. Caianiello

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