Octonion and Split Octonion Representation of SO(8) Symmetry

Abstract

The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The comparison of 8$\times$8 matrices with octonions has also been shown. The transformations of SO(8) symmetry are represented with the help of Octonions and split Octonions spinors.

References in corpus (3)

• Quaternion Octonion Reformulation of Quantum Chromodynamics
• Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges
• Interpretations of Octonion Wave Equations