Table of Contents
Preface to the English edition vii
Introduction 1
1 Symmetries of a quantum system 5
1.1 Rotation group in quantum mechanics 5
1.2 Electron in the Coulomb field 14
1.3 Broken symmetry 19
2 Observables of a quantum system 28
2.1 Deriving observables from a symmetry group 28
2.2 Quantum numbers of symmetry groups and their physical meaning 35
3 Lie groups and Lie algebras 39
3.1 Lie groups 39
3.2 Lie algebras 46
3.3 Representations of Lie groups 59
3.4 Universal enveloping algebras and Casimir operators 73
3.5 Tensor product of representations 76
4 The principles of particle classification 81
4.1 The concept of spin 81
4.2 Isotopic spin 85
4.3 SU(3) group-90
4.4 Baryon octet and decuplet 95
4.5 Mass formula in the SU(3) symmetry 101
4.6 SU(6) group 104
4.7 Classification principles in a quantum theory 108
5 The symmetry group of chemical elements 114
5.1 Description of the system of elements 114
5.2 The conformal group 119
5.3 A special representation of the conformal group 126
5.4 The symmetry group of the system of elements 131
5.5 Mass formula for atomic weights 141
6 Classification and chemical properties of elements 145
6.1 Small multiplets and chemical properties 145
6.2 Operators of chemical affinity 150
Appendix A Fock's energy spectrum of the hydrogen atom 158
A1 Schrödinger equation in the momentum representation 158
A2 Fock transformation 160
A3 Hydrogen spectrum 165
Appendix B Representations of some groups 169
B1 Local representations of SO(3) and SO(4) groups 169
B2 Spherical functions and reduction of representations 172
B3 Some representations of SU(3) group 179
References 182
