TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.030
TI  - Hyperquaternions and physics
PY  - 2023/11/24
UR  - https://scipost.org/SciPostPhysProc.14.030
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 030
A1  - Girard, Patrick R.
AU  - Pujol, Romaric
AU  - Clarysse, Patrick
AU  - Delachartre, Philippe
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysProc.14.030,
	title={{Hyperquaternions and physics}},
	author={Patrick R. Girard and Romaric Pujol and Patrick Clarysse and Philippe Delachartre},
	journal={SciPost Phys. Proc.},
	pages={030},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.030},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.030},
}