Article
Version 3
Preserved in Portico This version is not peer-reviewed
Extrinsic Quaternion Spin
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 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)
How to cite: Sanctuary, B. Extrinsic Quaternion Spin. Preprints 2023, 2023020055. https://doi.org/10.20944/preprints202302.0055.v3 Sanctuary, B. Extrinsic Quaternion Spin. Preprints 2023, 2023020055. https://doi.org/10.20944/preprints202302.0055.v3
Abstract
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. The reason for doing this is to introduce a bivector into the spin algebra. This modifies the Dirac equation equation which 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.
Keywords
foundations of physics; Dirac equation; spin; quantum theory; non-locality; helicity
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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