Spin with Hyper-helicity

Bryan Sanctuary

doi:10.20944/preprints202301.0571.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 January 2023 / Approved: 31 January 2023 / Online: 31 January 2023 (04:23:01 CET)
Version 2 : Received: 4 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (04:32:30 CEST)
Version 3 : Received: 14 June 2024 / Approved: 15 June 2024 / Online: 17 June 2024 (08:34:04 CEST)

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, afforded 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. The resulting spin equation separates into 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. We discuss some consequences.

Foundations of physics; Dirac equation; Spin; Quantum Theory; non-locality; helicity

Physical Sciences, Quantum Science and Technology

Comment 1

Received: 4 April 2023
Commenter: Bryan Sanctuary
Commenter's Conflict of Interests: Author

Comment: I updated the references, and a few clarifications

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Spin with Hyper-helicity

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