An Introduction to Field Quantization

International Series of Monographs in Natural Philosophy

Y. Takahashi, D. ter Haar

• Publisher: Pergamon
• Year: 2016
• Print ISBN:
  9780080128245
• eBook ISBN:
  9781483186276
• Topic: Physical Sciences
• Subtopic: Biology

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.

Table of contents

• Front Cover
• An Introduction to Field Quantization
• Copyright Page
• Table of Contents
• PREFACE
• CHAPTER I. INTRODUCTION
• CHAPTER II. NON-RELATIVISTIC FIELDS
• CHAPTER III. RELATIVISTIC FREE FIELDS
• CHAPTER IV. SOME ASPECTS OF LINEAR FIELD EQUATIONS
• CHAPTER V. QUANTIZATION OF RELATIVISTIC FREE FIELDS
• CHAPTER VI. TRANSFORMATION PROPERTIES OF FIELD OPERATORS
• CHAPTER VII. AN EXPLICIT CONSTRUCTION OF WAVE FUNCTIONS
• CHAPTER VIII. INTERACTING FIELDS
• READING GUIDE
• APPENDIX A: Solution of the Klein–Gordon equation and associated functions
• APPENDIX B: Dirac matrices
• APPENDIX C: A and d for various fields
• APPENDIX D: Formulae for 1/2 [ε(xo–'xo), F(∂)] (x-x' )
• APPENDIX E: Transition probability, cross-section and lifetime
• PROBLEMS
• REFERENCES
• INDEX