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Contents 8 Preface 14 1 Dirac Notations 16 1.1. Bra and Ket Vectors. Coordinate and Momentum Representations 16 1.2. Fock Representation. (Anti)holomorphic Representations 21 1.3. Clifford Algebra and Free Fermion Algebra 29 1.3.1. Clifford algebra 29 1.3.2. Fock representation for free fermion algebra 34 1.3.3. Grassmann algebra 37 2 Finite-Dimensional Representations of Lie Algebras su(2) and s(2,C) and Lie Groups SU(2) and SL(2,C) 44 2.1. Finite-Dimensional Representations of Lie Algebras su(2) and sl(2, C) 44 2.2. Differential Realization of Lie Algebra sl(2, C) and Highest Weight Representations 52 2.2.1. Realization of Lie algebra sl(2, C) in terms of differential operators 52 2.2.2. Highest weight representations of differential realizations of sl(2, C) 57 2.2.3. Coherent states for Lie algebra sl(2, C) 62 2.3. Finite-Dimensional Representations of Groups SU(2) and SL(2, C) 68 2.3.1. Parameterizations of Group SU(2) 68 2.3.2. Finite-dimensional representations of groups SU(2), SL(2, C) and SO(3). Tensor representations — Wigner functions 73 2.3.3. Spherical functions on S2 = SU(2)/U(1). Laplace operators on SU(2) and SU(2)/U(1) 83 2.4. Tensor Product of Representations

Author

Isaev, Alexey P; Rubakov, Valery A;

Language

EN