REAL ORTHOGONAL GROUPS

The following sections are included:

• Tensor Representations of SO(N)

  • Tensors of SO(N)

  • Irreducible Basis Tensors of SO(2ℓ + 1)

  • Irreducible Basis Tensors of SO(2ℓ)

  • Dimensions of Irreducible Tensor Representations

  • Adjoint Representation of SO(N)

  • Tensor Representations of O(N)

• Γ Matrix Groups

  • Property of Γ Matrix Groups

  • The Case N = 2ℓ

  • The Case N = 2ℓ + 1

• Spinor Representations of SO(N)

  • Covering Groups of SO(N)

  • Fundamental Spinors of SO(N)

  • Direct Products of Spinor Representations

  • Spinor Representations of Higher Ranks

  • Dimensions of the Spinor Representations

• Rotational Symmetry in N-Dimensional Space

  • Orbital Angular Momentum Operators

  • Spherical Harmonic Functions

  • Schrödinger Equation for a Two-body System

  • Schrödinger Equation for a Three-body System

  • Dirac Equation in (N + 1)-dimensional Space–time

• The SO(4) Group and the Lorentz Group

  • Irreducible Representations of SO(4)

  • Single-valued Representations of O(4)

  • The Lorentz Group

  • Irreducible Representations of L_p

  • The Covering Group of L_p

  • Classes of L_p

  • Irreducible Representations of L_h

• Exercises