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

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Abstract

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 \(\textit{C}\ell ^{\mathbb {R}}\)(4,2) and \(\textit{C}\ell ^{\mathbb {R}}\)(0,6) in the terms of Dirac \(\gamma \) 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.

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Acknowledgements

The author is much grateful for Profs. J. Keller and W. Rodrigues Jr. for the support of our investigations, see, e.g., [28, 51]. I must thank the unknown referee for useful remark, which helped to overcome the misleading notation in last column of the Table 1.

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  1. Institute of Electron Physics, National Academy of Sciences, Universitetska 21, Uzhgorod, 88000, Ukraine

    V. M. Simulik

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Simulik, V.M. On the Gamma Matrix Representations of SO(8) and Clifford Algebras. Adv. Appl. Clifford Algebras 28, 93 (2018). https://doi.org/10.1007/s00006-018-0906-3

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