K. Scharnhorst: *A special irreducible matrix representation
of the real Clifford algebra C(3,1)*. Journal of Mathematical Physics
**40**:7(1999)3616-3631 (DOI: 10.1063/1.532912)
[Humboldt University Berlin Preprint HUB-EP-97/83, arXiv:hep-th/9712113].
[INSPIRE record]

**Abstract**:
*4×4* Dirac (gamma) matrices [irreducible matrix representations of
the Clifford algebras *C(3,1)*, *C(1,3)*, *C(4,0)*] are an
essential part of many calculations in quantum physics. Although
the final physical results do not depend on the applied
representation of the Dirac matrices (e.g., due to the invariance
of traces of products of Dirac matrices), the appropriate
choice of the representation used may facilitate the analysis.
The present paper introduces a particularly symmetric real
representation of *4×4* Dirac matrices (Majorana representation)
which may prove useful in the future. As a by-product, a
compact formula for (transformed) Pauli matrices is found.
The consideration is based on the role played by isoclinic
2-planes in the geometry of the real Clifford algebra *C(3,0)*
which provide an invariant geometric frame for it. It can be
generalized to larger Clifford algebras.

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- Electronic copy of the preprint version - Humboldt University Berlin Preprint HUB-EP-97/83: arXiv:hep-th/9712113
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