Dual Hyperquaternion Poincare Groups

Résumé

A new representation of the Poincare groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor product of quaternion algebras (or a subalgebra thereof). This formalism yields a uniquely defined product and simple expressions of the Poincare generators, with immediate physical meaning, revealing the algebraic structure independently of matrices or operators. An extended multivector calculus is introduced (allowing a possible sign change of the metric or of the exterior product). The Poincare groups are formulated as a dual extension of hyperquaternion pseudo-orthogonal groups. The canonical decomposition and the invariants are discussed. As concrete example, the 4D Poincare group is examined together with a numerical application. Finally, the hyperquaternion representation is compared to the quantum mechanical one. Potential applications include in particular, moving reference frames and computer graphics.

Publication
In Advances in applied Clifford algebras
Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software.
Create your slides in Markdown - click the Slides button to check out the example.

Supplementary notes can be added here, including code, math, and images.

Patrick Clarysse
Patrick Clarysse
Chercheur CNRS (section 7) de CREATIS, Membre d’IEEE et de SFGBM

Responsable de la première équipe Imagerie Cœur-Vaisseaux-Poumons