Contents

Preface to the English edition

Introduction

1 Symmetries of a quantum system

1.1. Rotation group in quantum mechanics

1.2. Electron in the Coulomb field

1.3. Broken symmetry

2 Observables of a quantum system

2.1. Deriving observables from a symmetry group

2.2. Quantum numbers of symmetry groups and their physical meaning

3 Lie groups and Lie algebras

3.1. Lie groups

3.2. Lie algebras

3.3. Representations of Lie groups

3.4. Universal enveloping algebras and Casimir operators

3.5. Tensor product of representations

4 The principles of particle classification

4.1. The concept of spin

4.2. Isotopic spin

4.3. SU(3) group

4.4. Baryon octet and decuplet

4.5. Mass formula in the SU(3) symmetry

4.6. SU(6) group

4.7. Classification principles in a quantum theory

5 The symmetry group of chemical elements

5.1. Description of the system of elements

5.2. The conformal group

5.3. A special representation of the conformal group

5.4. The symmetry group of the system of elements

5.5. Mass formula for atomic weights

6 Classification and chemical properties of elements

6.1. Small multiplets and chemical properties

6.2. Operators of chemical affinity

Appendix A. Fock’s energy spectrum of the hydrogen atom

A1. Schrödinger equation in the momentum representation

A2. Fock transformation

A3. Hydrogen spectrum

Appendix B. Representations of some groups

B1. Local representations of SO(3) and SO(4) groups

B2. Spherical functions and reduction of representations

B3. Some representations of SU(3) group

References