Causality and dispersion relations / H. M. Nussenzveig.

Format:

Book

Author/Creator:

Nussenzveig, H. M. (Herch Moyses)

Series:

Mathematics in science and engineering ; v. 95.

Mathematics in science and engineering ; v. 95

Language:

English

Subjects (All):

Causality (Physics).

Dispersion relations.

Physical Description:

1 online resource (449 p.)

Place of Publication:

New York : Academic Press, 1972.

Language Note:

English

Summary:

Causality and dispersion relations

Contents:

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 Scattering2.3. 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 ScatteringReferences; 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 Potentials5.6. 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

A2. The Space D and Schwartz Distributions

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28886-5

9786612288869

0-08-095604-1

OCLC:

316566635