The Pauli Exclusion Principle

Preface Chapter 1 Historical Survey 1.1. Discovery of the Pauli Exclusion Principle and early developments 1.2. Further developments and still existing problems References Chapter 2 Construction of Functions with a Definite Permutation Symmetry 2.1. Identical particles in quantum mechanics and indistinguishability principle 2.2. Construction of permutation-symmetrical functions using the Young operators 2.3. The total wave functions as a product of spatial and spin wave functions 2.3.1 Two-particle system 2.3.2 General case of N-particle system References Chapter 3 Can the Pauli Exclusion Principle Be Proved? 3.1. Critical analysis of the existing proofs of the Pauli exclusion principle 3.2. Some contradictions with the concept of particle identity and their independence in the case of the multi-dimensional permutation representations References Chapter 4 Classification of the Pauli-Allowed States in Atoms and Molecules 4.1. Electrons in a central field 4.1.1 Equivalent electrons. L-S coupling 4.1.2. Additional quantum numbers. The seniority number 4.1.3 Equivalent electrons. j-j coupling 4.2. The connection between molecular terms and nuclear spin 4.2.1 Classification of molecular terms and the total nuclear spin 4.2.2 The determination of the nuclear statistical weights of spatial states 4.3. Determination of electronic molecular multiplets 4.3.1 Valence bond method 4.3.2 Degenerate orbitals and one valence electron on each atom 4.3.3 Several electrons specified on one of the atoms 4.3.4 Diatomic molecule with identical atoms 4.3.5 General case I 4.3.6 General case II References Chapter 5 Parastatistics, Fractional Statistics, and Statistics of Quasiparticles of Different Kind 5.1. Short account of parastatistics 5.2. Statistics of quasiparticles in a periodical lattice 5.2.1 Holes as collective states 5.2.2 Statistics and some properties of holon gas 5.2.3 Statistics of hole pairs 5.3 Statistics of Cooper's pairs 5.4 Fractional statistics 5.4.1 Eigenvalues of angular momentum in the three- and two-dimensional space 5.4.2 Anyons and fractional statistics References Appendix 1 Necessary Basic Concepts and Theorems of Group Theory A1.1 Properties of group operations A1.2 Representation of groups References Appendix 2 The Permutation Group A2.1 General information A2.2 The standard Young-Yamanouchi orthogonal representation References Appendix 3 The Interconnection Between Linear Groups and Permutation Groups. A3.1 Continuous groups A3.2 The three-dimensional rotation group A3.3 Tensor representations A3.4 Tables of the reductions of the representation to the group R3 References Appendix 4 Irreducible Tensor Operators A4.1 Definition A4.2 The Wigner-Eckart theorem References Appendix 5 Second Quantization References Index