Causality and Dispersion Relations

Name: Causality and Dispersion Relations
Brand: Academic Press
Price: 88.95 EUR
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Nussenzveig(Autor*in)

Nussenzveig(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

449 Seiten

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978-0-08-095604-6 (ISBN)

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Front Cover
Causality and Dispersion Relations
Copyright Page
Contents
Preface
Part I: CAUSALITY AND ANALYTICITY
Chapter 1. Causality and Dispersion Relations
1.1. Introduction
1.2. The Damped Harmonic Oscillator
1.3. Causality and Analyticity
1.4. Light Propagation in a Dielectric Medium
1.5. Physical Origin of Dispersion Relations
1.6. Titchmarsh's Theorem
1.7. Subtractions
1.8. Dispersion Relations and Distributions
1.9. The Kramers-Kronig Relation
1.10. The Optical Theorem
References
Chapter 2. Partial-Wave Dispersion Relations
2.1. Introduction
2.2. Classical Field: s-Wave Scattering
2.3. The Causality Condition
2.4. Analytic Continuation to I _
2.5. Product Expansion
2.6. Extension to Higher Angular Momenta
2.7. Nonrelativistic Quantum Scattering
2.8. The Schützer-Tiomno Causality Condition
2.9. Van Kampen's Causality Condition
2.10. The R-Function
2.11. Wigner's Causal Inequality
2.12. Completeness
References
Chapter 3. Dispersion Relations for the Total Scattering Amplitude
3.1. Introduction
3.2. Dispersion Relations for Fixed Scattering Angle
3.3. Dispersion Relations for Fixed Momentum Transfer
3.4. Fxtension to Nonrelativistic Quantum Scattering
References
Chapter 4. Physical Interpretation of S-Matrix Singularities
4.1. Introduction
4.2. Effects on the Cross Section
4.3. Complex Poles and Unstable States
4.4. Vibrating String and Oscillator
4.5. The Transient-Mode Propagator for the Schrüdinger Equation
4.6. Application to an Explicit Model
References
Part II: POTENTIAL SCATTERING
Chapter 5. Analytic Properties of Partial-Wave Amplitudes
5.1. Introduction
5.2. The Jost Function
5.3. Analytic Properties of the Jost Function
5.4. The Singularities of the S-Function
5.5. Cutoff Potentials
5.6. An Example: Square Well or Barrier
5.7. M ittag-Leffler and Transient-Mode Expansions
5.8. Extension to Higher Angular Momenta
References
Chapter 6. Analytic Properties of the Total Amplitude
6.1. Introduction
6.2. The Resolvent Operator in Banach Space
6.3. Analytic Properties of the Total Scattering Amplitude
6.4. High-Energy Behavior of the Scattering Amplitude
6.5. Dispersion Relations for Fixed Momentum Transfer
6.6. Analyticity in Momentum Transfer and Finite Range of the Interaction
References
Chapter 7. Regge Poles
7.1. Introduction
7.2. Regular and Irregular Solutions
7.3. The Jost Function and the S-Function
7.4. Properties of the Pole Distribution
7.5. Asymptotic Behavior of S(?,k) as 2, k) as │?│ 8
7.6. Watson Transformation and Analytic Continuation in cos ?
7.7. Regge Poles
References
Chapter 8. The Mandelstam Representation
8.1. Derivation of the Mandelstam Representation
8.2. The Unitarity Condition
8.3. Determination of the Scattering Amplitude from Mandelstam's Representation and Unitarity
8.4. Cutoff Potentials
References
Appendix A. Distribution Theory
A1. Introduction
A2. The Space D and Schwartz Distributions
A3. Operations with Distributions
A4. Differentiation of Distributions
A5. Product of Distributions
A6. Support of a Distribution
A7. Direct Product
A8. Convolution
A9. Fourier Transforms and the Space I
A10. Temperate Distributions and Their Fourier Transforms
A11. Fourier Transform of P(1/t) and Related Distributions
References
Appendix B. Passivity and Causality
Appendix C. Properties of Herglotz Functions
Appendix D. Properties of R-Functions
Appendix E. Asymptotic Time Behavior of Free Schrödinger Wave Packets
Appendix F. Compact Operators in Banach Space
Appendix G. Asymptotic Behavior of Green's Function
Appendix H. The Path ? (v)
Appendix I. Dispersion Relation for the Basic Mandelstam Integral
Author Index
Subject Index

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