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Quaternion Spin

Author

Listed:
  • Bryan Sanctuary

    (Department of Chemistry, McGill University, Montreal, QC H3A 0B8, Canada
    Retired Professor.)

Abstract

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, Q 8 , achieved by multiplying one of the gamma matrices by the imaginary number, i . The reason for doing this is to introduce a bivector into the spin algebra, which complexifies the Dirac field. It then separates into two distinct and complementary spaces: one describing polarization and the other coherence. The former describes a 2D structured spin, and the latter its helicity, generated by a unit quaternion.

Suggested Citation

  • Bryan Sanctuary, 2024. "Quaternion Spin," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1962-:d:1421424
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    References listed on IDEAS

    as
    1. M. Ahmadi & B. X. R. Alves & C. J. Baker & W. Bertsche & E. Butler & A. Capra & C. Carruth & C. L. Cesar & M. Charlton & S. Cohen & R. Collister & S. Eriksson & A. Evans & N. Evetts & J. Fajans & T. F, 2017. "Observation of the 1S–2S transition in trapped antihydrogen," Nature, Nature, vol. 541(7638), pages 506-510, January.
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