Includes bibliographical references and index.

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

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