Unitary Group Representations in Physics, Probability and Number Theory

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Note......Page 6
Contents......Page 8
Preface......Page 10
1. Introduction......Page 14
2. Representations of finite commutative groups......Page 18
Notes and References......Page 22
3. Characters and the decomposition of representations of finite groups that are not necessarily commutative......Page 23
Notes and References......Page 42
4. Preliminaries concerning infinite groups and measure spaces......Page 43
5. Compact groups and the Peter-Weyl theorem......Page 49
6. Locally compact commutative groups......Page 50
7. Direct integrals of unitary representations in the general case......Page 62
8. Primary representations and the von Neumann-Murray theory of factors......Page 67
9. Hilbert G-bundles, systems of imprimitivity, and induced representations......Page 77
10. The unitary representations of semi-direct products......Page 86
11. Unitary representations of general group extensions......Page 92
Notes and References (for Sections 4 through 11)......Page 96
12. Simple groups......Page 99
Notes and References......Page 108
13. The irreducible unitary representations of compact simple groups......Page 109
Notes and References......Page 120
14. The irreducible unitary representations of noncompact simple groups......Page 122
Notes and References......Page 140
15. Ergodic theory......Page 146
16. Applications to probability theory......Page 156
Notes and References (for Sections 15 and 16)......Page 170
17. The foundations of quantum mechanics......Page 172
Notes and References......Page 186
18. The quantum mechanics of one-particle systems......Page 187
Notes and References......Page 211
19. Particle interactions......Page 212
20. Bound states and the structure of matter......Page 232
Notes and References......Page 246
21. Collision theory and the S operator......Page 248
Notes and References......Page 259
22. Radiation, special relativity, and field theory......Page 262
Notes and References......Page 281
23. Temperature, heat, and thermodynamics......Page 285
24. Statistical mechanics and the many-body problem......Page 294
Notes and References......Page 315
25. Fourier analysis and analytic functions......Page 316
26. Number theory......Page 325
Notes and References......Page 339
27. Diophantine equations and Fourier analysis......Page 341
Notes and References......Page 352
28. Semi-direct products, algebraic number fields, and diophantine equations......Page 353
29. Quadratic forms and automorphic forms......Page 367
Notes and References......Page 375
30. Automorphic forms and group representations......Page 376
Notes and References......Page 393
31. The Weil-Siegel Formula......Page 396
Notes and References......Page 407
Index......Page 408