Introduction to Field Quantization (eBook)

International Series of Monographs in Natural Philosophy

Y. Takahashi (Autor)

D. ter Haar (Herausgeber)

eBook Download: PDF

2016 | 1. Auflage
310 Seiten
Elsevier Science (Verlag)
9781483186276 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 20.9.2016
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik
• ISBN-13: 9781483186276 / 9781483186276