Extrinsic Quaternion Spin

Bryan Sanctuary

doi:10.20944/preprints202302.0055.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 1 February 2023 / Approved: 3 February 2023 / Online: 3 February 2023 (03:51:33 CET)
Version 2 : Received: 31 March 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (03:01:35 CEST)
Version 3 : Received: 26 January 2024 / Approved: 29 January 2024 / Online: 29 January 2024 (08:47:38 CET)
Version 4 : Received: 18 May 2024 / Approved: 20 May 2024 / Online: 20 May 2024 (12:37:38 CEST)
Version 5 : Received: 17 June 2024 / Approved: 18 June 2024 / Online: 18 June 2024 (08:15:32 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, Theoretical Physics

Comment 1

Received: 3 April 2023
Commenter: Bryan Sanctuary
Commenter's Conflict of Interests: Author

Comment: Following feedback, I have made changes to improve the clarity of this paper

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Extrinsic Quaternion Spin

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