Quaternion Spin
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908289706491904 |
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| author | Sanctuary, Bryan |
| author_facet | Sanctuary, Bryan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternion Spin Sanctuary, Bryan General Physics 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. |
| title | Quaternion Spin |
| topic | General Physics |
| url | https://arxiv.org/abs/2503.22761 |