Matrix Representations of Clifford Algebras

Article 03910 introduced Clifford algebra, which can be used to construct the spin group (article 08264), a special double cover of the part of the group of Lorentz transformations that is generated by pairs of reflections. Clifford algebras admit matrix representations in which each basis vector is represented by a Dirac matrix. This article shows how to construct matrix representations for Clifford algebras of any signature in any number of dimensions.

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Revision history

2023-10-01 (fixed a copy-paste error, clarified notation in one section, changed one section title)
2023-06-02 (added a footnote with another warning about language, made the abstract more precise)
2023-05-28 (deleted an extra word, clarified a footnote, added a sentence about hermitian/antihermitian)
2023-05-14 (added a cross-reference to the abstract, reworded one phrase for clarity, fixed an incorrect word (odd → even) in one section and separated the section into two to improve readability)
2023-05-08 (first version)

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updated 2024-04-16

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Matrix Representations of Clifford Algebras

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