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Hyperquaternions and physics

Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre

SciPost Phys. Proc. 14, 030 (2023) · published 24 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


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.

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