Naimark / Farahat Linear Representations of the Lorentz Group

1. Auflage 2014
ISBN: 978-1-4831-8498-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 63, 464 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

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.

Autoren/Hrsg.

Naimark, M. A.

Farahat, H. K.

Inhaltsverzeichnis

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