2023-06-02   87696

(In)equivalence of Irreducible Representations of Clifford Algebras

Given an irreducible matrix representation of a Clifford algebra, we can get another one by replacing every Dirac matrix with its negative, with its complex conjugate, with its transpose, or any composition of these. These representations may or may not be equivalent to each other (related to each other by a linear transformation), depending on the number d of dimensions of the vector space that generates the Clifford algebra, and depending on the signature. This article determines which ones are equivalent to each other for each number of dimensions and each signature. When d is even, the answer is simple: they are all equivalent to each other. When d is odd, the pattern is more complicated.

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www.cphysics.org updated 2024-07-11