Linear Representations of the Lorentz Group (eBook)

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