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Hyperquaternions and Physics
by Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre
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Submission summary
| Authors (as registered SciPost users): | Patrick Girard |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202211_00033v2 (pdf) |
| Date submitted: | 2023-01-06 10:08 |
| Submitted by: | Girard, Patrick |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The paper develops, within a new representation of Clifford algebras in terms of tensor products of quaternions called hyperquaternions, several applications. The first application is a quaternion 2D representation in contradistinction to the frequently used 3D one. The second one is a new representation of the conformal group in (1+2) space (signature +--) within the Dirac algebra C5(2,3)=C*H*H subalgebra of H*H*H (* tensor product). A numerical example and a canonical decomposition into simple planes are given. The third application is a classification of all hyperquaternion algebras into four types, providing the general formulas of the signatures and relating them to the symmetry groups of physics.
List of changes
1 - In the Introduction, line 9, there is an obvious mistake: the signature of
the (1+2) space is +—-, instead of +-.
This has been corrected.