Takahashi / Ter Haar An Introduction to Field Quantization

International Series of Monographs in Natural Philosophy
1. Auflage 2016
ISBN: 978-1-4831-8627-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 310 Seiten, Web PDF

An Introduction to Field Quantization is an introductory discussion of field quantization and problems closely related to it. Field quantization establishes a commutation relation of the field and finds an operator in such a manner that the Heisenberg equation of motion is satisfied. This book contains eight chapters and begins with a review of the quantization of the Schroedinger field and the close relation between quantized field theory and the many-body theory in quantum mechanics. These topics are followed by discussions of the quantization of the radiation field and the field of lattice vibrations in a solid. The succeeding chapter deals with the familiar linear equations in relativistic field theory and the deduction of certain spin independent theories, which these fields have in common. Other chapter explores the derivation technique of the conservation laws for fields with arbitrary spin directly from the field equations without explicit recourse to Noether's theorem using a configuration space version of the generalized Ward identity. The discussion then shifts to the relativistic quantization method applicable to any field with arbitrary spin; the transformation of various fields under the Lorentz transformation; and a general method for constructing wave functions explicitly, as well as the application of this method to several examples. The concluding chapter focuses on the quantization of interacting fields. This book will prove useful to physicists and researchers.

Autoren/Hrsg.

Takahashi, Y.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;An Introduction to Field Quantization;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;10
6;CHAPTER I. INTRODUCTION;14
6.1;1. Introductory considerations;14
6.2;2. Creation and annihilation operators;19
7;CHAPTER II. NON-RELATIVISTIC FIELDS;24
7.1;1. The Schroedinger field;24
7.2;2. The radiation field;34
7.3;3. Harmonic lattice vibrations;48
8;CHAPTER III. RELATIVISTIC FREE FIELDS;58
8.1;1. Notation and conventions;58
8.2;2. Fields with spin 0,1, and 2;61
8.3;3. Fields with spin 1/2 and 3/2;69
8.4;4. A general field equation of first order;76
8.5;5. The Bargmann-Wigner fields;79
8.6;6. Massless fields;85
9;CHAPTER IV. SOME ASPECTS OF LINEAR FIELD EQUATIONS;91
9.1;1. Conservation laws and the first identity;91
9.2;2. The Klein-Gordon divisor and the second identity;103
10;CHAPTER V. QUANTIZATION OF RELATIVISTIC FREE FIELDS;114
10.1;1. Wave functions and their normalization;114
10.2;2. Quantization—A general theory;125
10.3;3. Quantization—examples;140
10.4;4. Quantization of massless fields;149
11;CHAPTER VI. TRANSFORMATION PROPERTIES OF FIELD OPERATORS;162
11.1;1. Lorentz transformations;162
11.2;2. Uniqueness of generators of inhomogeneous Lorentz transformation;173
11.3;3. Discrete transformations;178
11.4;4. Substitution law;201
12;CHAPTER VII. AN EXPLICIT CONSTRUCTION OF WAVE FUNCTIONS;203
12.1;1. A general theory;203
12.2;2. Examples;206
13;CHAPTER VIII. INTERACTING FIELDS;214
13.1;1. The quantization of interacting fields;214
13.2;2. Examples;233
13.3;3. Selected topics;241
14;READING GUIDE;268
15;APPENDIX A: Solution of the Klein–Gordon equation and associated functions;270
16;APPENDIX B: Dirac matrices;274
17;APPENDIX C: A and d for various fields;280
18;APPENDIX D: Formulae for 1/2 [e(xo–'xo), F(.)] .(x-x' );284
19;APPENDIX E: Transition probability, cross-section and lifetime;287
20;PROBLEMS;292
21;REFERENCES;302
22;INDEX;306