Octonion and Split Octonion Representation of SO(8) Symmetry

TL;DR

This paper explores the representation of SO(8) symmetry using 8x8 matrices derived from Pauli and Gamma matrices, and compares these with octonions, also employing octonion-based spinors for transformations.

Contribution

It introduces a novel 8x8 matrix representation of SO(8) symmetry using Pauli and Gamma matrices and connects it with octonion and split octonion frameworks.

Findings

8x8 matrix representation of SO(8) constructed

Comparison between matrix representation and octonions shown

Transformations expressed using octonion and split octonion spinors

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.