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Pauli-Dirac matrix generators of Clifford Algebras

Abstract

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C2 is generated by two Pauli matrices iσ2 and iσ3; C3 is generated by the three Pauli matrices σ1, σ2, σ3; C4 is generated by four Dirac matrices γ0, γ1, γ2, γ3 and C5 is generated by five Dirac matrices iγ0, iγ1, iγ2, iγ3, iγ5. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.

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Supported by the National Science Foundation under Grant ISP-80-11451.

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Poole, C.P., Farach, H.A. Pauli-Dirac matrix generators of Clifford Algebras. Found Phys 12, 719–738 (1982). https://doi.org/10.1007/BF00729808

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Keywords

  • Closed Form
  • Matrix Generation
  • Recent Article
  • Product Method
  • Clifford Algebra