Intro -- Title Page -- Copyright -- Contents -- 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-Symmetric 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 Multidimensional Pe... -- 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 A: Necessary Basic Concepts and Theorems of Group Theory -- A.1 Properties of Group Operations -- A.1.1 Group Postulates -- A.1.2 Examples of Groups -- A.1.3 Isomorphism and Homomorphism -- A.1.4 Subgroups and Cosets -- A.1.5 Conjugate Elements. Classes -- A.2 Representation of Groups -- A.2.1 Definition -- A.2.2 Vector Spaces -- A.2.3 Reducibility of Representations -- A.2.4 Properties of Irreducible Representations -- A.2.5 Characters -- A.2.6 The Decomposition of a Reducible Representation -- A.2.7 The Direct Product of Representations -- A.2.8 Clebsch-Gordan Coefficients -- A.2.9 The Regular Representation -- A.2.10 The Construction of Basis Functions for Irreducible Representation -- References -- Appendix B: The Permutation Group -- B.1 General Information -- B.1.1 Operations with Permutation -- B.1.2 Classes -- B.1.3 Young Diagrams and Irreducible Representations -- B.2 The Standard Young-Yamanouchi Orthogonal Representation -- B.2.1 Young Tableaux -- B.2.2 Explicit Determination of the Matrices of the Standard Representation -- B.2.3 The Conjugate Representation -- B.2.4 The Construction of an Antisymmetric Function from the Basis Functions for Two Conjugate Representations -- B.2.5 Young Operators -- B.2.6 The Construction of Basis Functions for the Standard Representation from a Product of N Orthogonal Functions -- References -- Appendix C : The Interconnection between Linear Groups and Permutation Groups -- C.1 Continuous Groups -- C.1.1 Definition.