Linear Representations of the Lorentz Group (eBook)

M. A. Naimark (Autor)

H. K. Farahat (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
464 Seiten
Elsevier Science (Verlag)
978-1-4831-8498-2 (ISBN)

Infos

Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.

Inhalt

Front Cover 1
Linear Representations of the Lorentz Group 4
Copyright Page 5
Table of Contents 
6 
PREFACE 12
CHAPTER I. THE THREE-DIMENSIONAL ROTATION GROUP AND THE LORENTZ GROUP 16
§ 1. The Three-dimensional Rotation Group 16
§ 2. The Lorentz Group 33
CHAPTER II. THE REPRESENTATIONS OF THE THREE-DIMENSIONAL ROTATION GROUP 40
§ 3. The Basic Concepts of the Theory of Finite-dimensional Representations 40
§ 4. Irreducible Representations of the Three-dimensional Rotation Group in Infinitesimal Form 46
§ 5. The Realization of Finite-dimensional Irreducible Representations of the Three-dimensional Rotation Group 65
§ 6. The Decomposition of a Given Representation of the Three-dimensional Rotation Group into Irreducible Representations 78
CHAPTER III. IRREDUCIBLE LINEAR REPRESENTATIONS OF THE PROPER AND COMPLETE LORENTZ GROUPS 104
§ 7. The Infinitesimal Operators of a Linear Representation of the Proper Lorentz Group 104
§ 8. Determination of the Infinitesimal Operators of a Representation of the Group © + 118
§ 9. The Finite-dimensional Representations of the Proper Lorentz Group 135
§ 10. Principal Series of Representations of the Group 153
§ 11. Description of the Representations of the Principal Series and of Spinor Representations by means of the Unitary Group 169
§ 12. Complementary Series of Representations of the Group 185
§ 13. The Trace of a Representation of the Principal or Complementary Series 203
§ 14. An Analogue of Plancherel's Formula 225
§ 15. A Description of all the Completely Irreducible Representations of the Proper Lorentz Group 249
§ 16. Description of all the Completely Irreducible Representations of the Complete Lorentz Group 312
CHAPTER IV. INVARIANT EQUATIONS 342
§ 17. Equations Invariant with Respect to Rotations of Three-dimensional Space 342
§ 18. Equations Invariant with Respect to Proper Lorentz Transformations 362
§ 19. Equations Invariant with Respect to Transformations of the Complete Lorentz Group 388
§ 20. Equations Derived from an Invariant Lagrangian Function 397
APPENDIX 438
REFERENCES 456
INDEX 460
VOLUMES PUBLISHED IN THE SERIES IN PURE AND APPLIED MATHEMATICS 464

Produkt-Details

• Erscheint lt. Verlag: 15.7.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• ISBN-10: 1-4831-8498-6 / 1483184986
• ISBN-13: 978-1-4831-8498-2 / 9781483184982