Quaternion Spin

Bryan Sanctuary

doi:10.3390/math12131962

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arXiv · 2503.22761

Quaternion Spin

Bryan Sanctuary

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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.

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Bryan Sanctuary. 2025-03-27. Quaternion Spin. https://doi.org/10.3390/math12131962

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