The gamma matrix representation of 28-dimensional SO(8) algebra, which contains the standard and additional spin operators, is under consideration. The 64-dimensional representations of the Clifford algebras C R (4,2) and C R (0,6) in the terms of Dirac γ matrices are considered as well. The SO(8) and Clifford algebras are determined as the algebras over the field of real numbers. The relationships between the suggested representations of the SO(8) and Clifford algebras are investigated. The role of matrix representations of such algebras in the quantum field theory is discussed briefly. Recent failed interpretation is overcome.

V. M. Simulik

Advances in Applied Clifford Algebras

ADVANCES IN APPLIED CLIFFORD ALGEBRAS (AACA) 在 CLIFFORD 代数及其在数学、物理、工程和相关领域的其他分支中的应用领域发表高质量的同行评审研究论文以及说明性和调查性文章。该杂志确保快速出版，分为六个部分：分析、微分几何和狄拉克算子、数学结构、理论和数学物理、应用和书评。

The journal "Advances in Applied Clifford Algebras" focuses on Clifford algebras and their applications in mathematics, physics, engineering, and related fields. It publishes high-quality peer-reviewed research papers, as well as expository and survey articles, ensuring rapid publication. The journal is divided into six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.

《Advances in Applied Clifford Algebras》期刊专注于克利福德代数及其在数学、物理、工程及相关领域的应用。该期刊发表高质量的同行评审研究论文，以及说明性和调查性文章，确保快速出版。期刊内容分为六个部分：分析、微分几何与狄拉克算子、数学结构、理论与数学物理、应用以及书评。

Category	Quartile
数学	2
数学, 应用数学	2
数学, 物理数学物理	2

On the Gamma Matrix Representations of SO(8) and Clifford Algebras

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	3