Hyperquaternions and physics
Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre
SciPost Phys. Proc. 14, 030 (2023) · published 24 November 2023
- doi: 10.21468/SciPostPhysProc.14.030
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Proceedings event
34th International Colloquium on Group Theoretical Methods in Physics
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 $C_(2,3) \simeq $$\mathbb{C\otimes H\otimes H}$ subalgebra of $\mathbb{H\otimes H\otimes H}$. 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.
Cited by 1
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Patrick R. Girard,
- 2 Romaric Pujol,
- 1 Patrick Clarysse,
- 1 Philippe Delachartre
- 1 Université de Lyon / University of Lyon
- 2 Institut National des Sciences Appliquées de Lyon / National Institute of Applied Sciences of Lyon [INSA]